this is a slav defense dude. I don't know the theory but I guess somehow a6 is the best move and you want to play Bf5 and dxc4 in the future, maybe I am wrong, but this is all I know about slav
Caro-Kann

I wouldn't play caro kann against c4, that kinda defeats the point of it doesn't it? Isn't it meant as an e4 defense?
1.c4 c6 2.Nc3 d5 3.e3 will likely transpose into the Slav/Semi-Slav defense, although 3...e5 is an independent option (as mentioned above by play4fun64). Unless White plays 2.e4, there is no way for Black to ever force a transposition into the Caro.

OP, are you running into a lot of English players?
I always felt it was rare. The CK is a solid defense from what I have been experiencing as an English player.
I have two lines prep against the CK but rarely run into it.

After those four moves, I think that is the post at which shanky calls it the “meran without d4”.
There all also other move orders including 1.Nf3

... opponents use the Caro-Kann as a crutch because they can't play decent OTB chess. ...
Them's fightin' words, partner.
*Cracks knuckles.*

it is true. that bumbling fool alireza plays the caro kann as one of his primary responses to e4 and he knows nothing about otb chess. perhaps one day when he is no longer a child he will learn how a real man plays.
i used to play it but now do only rarely. perhaps i need the crutches

I don't think I've encountered it, however, I think I'd be inclined to go a Slav black London against it. Close the triangle with the light square bishop outside the chain. Castle long and undermine his advanced pawns. That's just intuition though. Any expert input on that approach?
The other thing that 'springs' to mind is Cambridge Springs Queens Gambit Declined line. Any input?
I know I actually need to put in some solid hours study on black, but I only get silly snippets of free time lately. I'm just throwing this out there to get some inspiration/advice from better players who AREN'T Caro Kann/Slav haters, regarding the OP's interesting question.
What do you play as black after c4 c6 Nc3 d5 e3?