No I mean with e5 and d3. It's a weird setup, but someone has liked to use it on me in blitz and now black can't attack the d4 point. Does black eventually play ...d4?
2. f4

An interesting question. I did find a fun game where Tal faced this setup--eventually (as black) he did push to d4, and managed to gain control over e4 via a timely ...f5. As might be expected with a semi-closed center, most of the later play centers on flank attacks and knight hopping.
A decidedly un-Tal-like game, at least from those game's of the Eighth World Champion that I've seen.

A couple months ago, I switched back to using 1. e4. Against 1... e5, I normally play Ruy Lopez and I win most of my games with it. Every once in a while I'll play King's Gambit (2. f4) and I also win most of my games with this.
However, I am fairly weak against other black responses. I have for some time now been looking for variations in many openings that will hopefully lead me to victory at least half of the time. However, I don't have the time to study every single variation of every single opening to see which one is the best. That's why I've come up with a solution that I hope will work.
My solution is to play 1. e4 1... ANY 2. f4. This is an aggressive move that takes control of the center and is very helpful for future kingside attacks. So far I have only used this move against computers (with more success than playing what I normally do), but I'd like to try it against real people. If you are skilled at one of the following openings, please challenge me to a game in that opening (I'm white. You can choose whether it's rated or unrated. Time Control 3 Days/Move). I will use 2. f4 against the opening.
Sicilian Defense (1... c5)
French Defense (1... e6)
Pirc Defense (1... d6)
Caro-Kann (1... c6)
Owen's Defense (1... b6)
Modern Defense (1... g6)
Nimzowitsch Defense (1... Nc6)
EDIT: King Pawn Game (1... e5)
In my opinion it doesn't make sense to be playing 2.f4 against everything as you aren't even getting into vaguely similar positions against any of Black's responses. If you know the plans quite well for the King's Gambit, when you play 2.f4 against the Sicilian for instance you aren't really cutting down on any work, you'll just have to prepare equally as hard for an entirely different opening: the Grand Prix Attack. If you want to cut down on study time and get lots of King-Side attacks I'd recommend switching instead to a "pattern based opening" such as The Stonewall, Torre, Colle or London system. Or combine the various systems as they all are very similar to each other.. However if Black plays correctly against any of these don't expect to get much of an objective advantage straight out of the opening. But in my opinion, at below Master level having the advantage is way over-rated anyway..

anyway on e4, > c6 or c5 or e5 i play as white as second move: f4. and then always play as third move: e5. Even if after e4, d5 occurs right away i play e5. of course i am far from perfect or technical high level but for me it is fun. i just came up with it cause i like the kings gambit so much. However one advice for white. dont play d4 out in the open. only to close it might black play c5 - c4. leave the center and indeed do some crazy stuff at the kingsside. :) if i usually survive attacks on the queenside, which black often tries then there is a chance of winning. For now i dont have good results with Bg2 to counter the diagonal pressure especially when i rush my kingspawns towards the black kingside. So for now somehwere in the opening i play the Be2 thing. a bit boring but like the kings gambit it is nice if you can sacrifice that one later :) see link above.

It's almost certainly a stupid idea, but 2. f4 in response to the Scandinavian looks like it could be fun.
Came to the discussion as I started to wonder if 2.f4 against Pirc could work. In same cases it transposes in a kind of closed Grand Prix attack. According to databases f4 might be playable.
When it comes to 2. f4 against Sicilian I don't think that it is particularly smart move as it just transposes into a bad line of of Grand Prix Attack for white if black plays d5. Nc3 is the correct move like some people here already mentioned. Then again even in that case Black has to know his homework to get an upperhand - I for example don't really have anything prepared against 2.f4 if I play Sicilian as normally only weaker players play it.
But if you want to play only 1 move start playing the Sniper on both colours. As Black first move always g6 and with white g3.

A couple months ago, I switched back to using 1. e4. Against 1... e5, I normally play Ruy Lopez and I win most of my games with it. Every once in a while I'll play King's Gambit (2. f4) and I also win most of my games with this.
However, I am fairly weak against other black responses. I have for some time now been looking for variations in many openings that will hopefully lead me to victory at least half of the time. However, I don't have the time to study every single variation of every single opening to see which one is the best. That's why I've come up with a solution that I hope will work.
My solution is to play 1. e4 1... ANY 2. f4. This is an aggressive move that takes control of the center and is very helpful for future kingside attacks. So far I have only used this move against computers (with more success than playing what I normally do), but I'd like to try it against real people. If you are skilled at one of the following openings, please challenge me to a game in that opening (I'm white. You can choose whether it's rated or unrated. Time Control 3 Days/Move). I will use 2. f4 against the opening.
Sicilian Defense (1... c5)
French Defense (1... e6)
Pirc Defense (1... d6)
Caro-Kann (1... c6)
Owen's Defense (1... b6)
Modern Defense (1... g6)
Nimzowitsch Defense (1... Nc6)
EDIT: King Pawn Game (1... e5)
What about 1...d5??

A couple months ago, I switched back to using 1. e4. Against 1... e5, I normally play Ruy Lopez and I win most of my games with it. Every once in a while I'll play King's Gambit (2. f4) and I also win most of my games with this.
However, I am fairly weak against other black responses. I have for some time now been looking for variations in many openings that will hopefully lead me to victory at least half of the time. However, I don't have the time to study every single variation of every single opening to see which one is the best. That's why I've come up with a solution that I hope will work.
My solution is to play 1. e4 1... ANY 2. f4. This is an aggressive move that takes control of the center and is very helpful for future kingside attacks. So far I have only used this move against computers (with more success than playing what I normally do), but I'd like to try it against real people. If you are skilled at one of the following openings, please challenge me to a game in that opening (I'm white. You can choose whether it's rated or unrated. Time Control 3 Days/Move). I will use 2. f4 against the opening.
Sicilian Defense (1... c5)
French Defense (1... e6)
Pirc Defense (1... d6)
Caro-Kann (1... c6)
Owen's Defense (1... b6)
Modern Defense (1... g6)
Nimzowitsch Defense (1... Nc6)
EDIT: King Pawn Game (1... e5)
What about 1...d5??
It'll just give Black the advantage after 2...dxe4 for zero compensation.

You can get f4 in against a lot of those defenses without showing your hand too early. Against sicilian go 2. Nc3 to rule out d5 and go into a main line Grand Prix. Pirc/modern I believe the fourth move is f4? Maybe a bishop move before then I'm not sure but anyway that'll get you an Austrian attack. French Winawer is pretty aggressive and f4 is more than likely to come(though I play the Steinitz as black against Nc3 so I see it a lot, and really don't know the Bb4 stuff). b6 is bound to go out of theory pretty quick so sure, why not f4. Against the Caro it seems a little weird to me, maybe f3, fantasy variation. And then the four pawns against Alekhine's. This at least gives you some more main line stuff to check out from master games

You can get f4 in against a lot of those defenses without showing your hand too early. Against sicilian go 2. Nc3 to rule out d5 and go into a main line Grand Prix. Pirc/modern I believe the fourth move is f4? Maybe a bishop move before then I'm not sure but anyway that'll get you an Austrian attack. French Winawer is pretty aggressive and f4 is more than likely to come(though I play the Steinitz as black against Nc3 so I see it a lot, and really don't know the Bb4 stuff). b6 is bound to go out of theory pretty quick so sure, why not f4. Against the Caro it seems a little weird to me, maybe f3, fantasy variation. And then the four pawns against Alekhine's. This at least gives you some more main line stuff to check out from master games
Other than the Caro, playing an early f4 is certainly playable. However, you can't really play 1.e4 and 2.f4 against almost every Black defense possible, which is what the OP suggests. Really, the only moves that 2.f4 is truly playable against are e5, e6, and c5, and out of those three it's "best" (as in the most playable, which isn't saying too much) against e5, the King's Gambit.

The fact that 1.e4 d6 2.f4 d5!? is a plausible defense for Black should tell you something about the merits of 2.f4. There are plenty of options for you on later moves to develop with f4, there is no need to commit yourself to a universal system where you play it on move 2, unless you are developing your bullet opening repertoire and you want to include 2.f4 as a premove. But I assume you're interested in learning and playing good chess.
Personally I've played 1.e4 e6 2.f4 several times. I like Advance-style positions but the traditional move order with 2.d4 is troublesome for White.
I assume you mean white playing 3 d3 rather than 3 e5. It's not a choice that's well represented in the databases, and I suspect we'd see a lot of draws following 3...dxe4 4 dxe4 Qxd1+ 5 Kxd1. Not that white scores well with 1 e4 e6 2 f4 d5 3 e5: just 46.4%, according to Chessbase.