#1
1 e4 e6 2 d4 d5 3 Nc3 c5? is no good. 3...Bb4, 3...Nf6, 3...Nc6 are better.
Yes, there are some similarities between the French and the Queen's Gambit Declined 1 d4 d5 2 c4 e6 e.g. Bc8 hemmed in by pawn chain f7-e6-d5.
If you are talking about the Slav Defence 1 d4 d5 2 c4 c6, then the Caro-Kann 1 e4 c6 2 d4 d5 is more similar: Bc8 is free to move, but ...Nc6 is not possible as pawn c6 is obstructing. Both have the pawn chain b7-c6-d5.
If I like playing the Queen's Gambit should I play the French defense too?
I play both. I fail to see similarities.
When I say similarities I mean they can both have an e pawn pushed one square as well as c and d pawns that are pushed two squares. Aside from both openings also being considered solid and positional that is it(that I can see). Also that does not answer the question, but since you play both I believe you can answer the question.
#1
1 e4 e6 2 d4 d5 3 Nc3 c5? is no good. 3...Bb4, 3...Nf6, 3...Nc6 are better.
Yes, there are some similarities between the French and the Queen's Gambit Declined 1 d4 d5 2 c4 e6 e.g. Bc8 hemmed in by pawn chain f7-e6-d5.
If you are talking about the Slav Defence 1 d4 d5 2 c4 c6, then the Caro-Kann 1 e4 c6 2 d4 d5 is more similar: Bc8 is free to move, but ...Nc6 is not possible as pawn c6 is obstructing. Both have the pawn chain b7-c6-d5.
I just made random moves for the diagram to show what I meant, but if I do play the french I will try to keep that in mind. I know you mentioned the slav and caro kann since they are much more similar than the comparison I made with the french and Queens gambit, but that does not answer the question. I get that the question may be hard to understand if read wrong or too quickly. What I I tried to ask was if one likes the Queens gambit should they also consider playing the french and vice versa.

me as well, dont see much similarities.
french is a black opening, qg is a white opening.
ideas and defenses are quite different. endgame pawn structures are different. you can see minority attack concept in qgd games, there is no such thing in french.
you usually see Kid in qgd..
well idk, i dont see any similarities. but why not.. you can play and enjoy both.. in different games.

This game came from a Queen's Pawn opening and resulted in a reversed French. Maybe it will contribute to your efforts to connect these two opening systems..

Yeah, they're really different openings.
But anyway, maybe there's a lesson in here somewhere. For example, the pattern you've noticed is useful in many different openings when your opponent has put at least one pawn in the center... and that is you often want to attack that center pawn with a pawn of your own.
In the french you play c5 against white's d pawn.
In the QG you play c4 against black's d pawn.
But for example, in 1.e4 e5 games both players are happy to play their d pawn two squares forwards when possible (depending on the opening, sometimes it takes more preparation than others).
These moves are called pawns breaks by the way. They open lines (meaning files, ranks, and diagonals) to be used by your non-pawns. The basic flow of a game might be described by staking a claim in the center, developing your non-pawns (including castling), and then playing a pawn break in the center to open line for your developed pieces.
#5
"if one likes the Queens gambit should they also consider playing the french and vice versa."
++ Yes, if you like 1 d4 d5 2 c4 as white and 1 d4 d5 2 c4 e6 as black, then it makes sense to play 1 e4 e6 2 d4 d5 3 Nc3 Nf6 as black as the pawn structures are similar: f7-e6-d5 and thus experience with one benefits the other.

#5
"if one likes the Queens gambit should they also consider playing the french and vice versa."
++ Yes, if you like 1 d4 d5 2 c4 as white and 1 d4 d5 2 c4 e6 as black, then it makes sense to play 1 e4 e6 2 d4 d5 3 Nc3 Nf6 as black as the pawn structures are similar: f7-e6-d5 and thus experience with one benefits the other.
You're too high rated to talk about a "pawn structure" by only looking at one side's pawns... stop it.
It's like when beginners ask if it's ok to still play the Spanish opening if their opponent doesn't play ...e5
#11
++ You can talk and analyse pawn structures from one side only
Isolated queen's pawn: a2-b2-d4-f2-g2-h2
Stonewall: a7-b7-c6-d5-e6-f5-g7-h7
King's Indian: a7-b7-c7-d6-e5-f7-g6-h7
There are similar ideas after 1 e4 e6 2 d4 d5 and 1 d4 d5 2 c4 e6, like preparing ...c5 and like finding a way to activate Bc8
By looks the setup black has in the French resembles white's setup in the Queens gambit(to me anyways). since there is a similarity would anyone recommend playing the other as well if they play one of the openings mentioned?
*Don't answer the question anymore, I've made my own decision on it. I also don't want to waste my time reading responses that don't answer the question.*
Hopefully the diagrams work alright. Ignore the move order