is the reti gambit a good option (as white) vs. the French, in rapid timing or longer, compared to t

Your question doesn't make any sense.
Reti gambit is a line in French defense.
What on earth Caro Kan has to do with it?
Do you wat to know if Reti gambit in French defense is better than Caro Kan?
Yes it is better than Caro Kan and worst than Nimzo Indian.
Sorry, that was badly phrased. I've heard you can use the same set up as white against the caro kan e4,b3,Bb2.
what I was trying to ask is whether the reti gambit, is a good opening for white in rapid time control?
secondly, is whites set up (e4,b3,Bb2) is a good way to play against the Caro kan?
sorry for the confusion

There are some significant differences that make 2.b3 less efficient against Caro Kan.
The main one is that white doesn't have the quick g4 that he usually has against French defense because the pawn simply drops.Since that is the move white usually uses to complicate matters , without it you aren't going to get the tactical blunderfest that you want.
So 2.b3 is interesting against French defense but rather uninteresting against Caro Kan(still not bad).
Maybe you would be interested to use the Hillbilly attack against Caro Kan.
https://www.chess.com/article/view/the-birth-and-development-of-the-hillbilly-attack
I'll definitely check that out, thanks.
any input on the reti gambit?

The Hillbilly Attack is a poor choice if you want to attack the Caro. It should be noted that Magnus Carlsen got a worse position out of the opening against Evgeny Tomashevsky. I imagine Tomashevsky only lost due to time pressure as it was a blitz game. There are much more interesting lines (and much more deadly!) that are available such as 1.e4 c6 2.d4 d5 3.Nc3 dxe4 4.Nxe4 Bf5 5.Ng3 Bg6 6.h4 h6 7.Nh3 with ideas of Nh3-f4 and Ng3-h5 with potential sacrifices coming.
1.e4 e6 2. b3 d5 3. Bb2 dxe4
is the reti gambit a good option (as white) vs. the French, in rapid timing or longer, compared to the normal lines? Or the caro-kan?