The Caro-Kann defence
Now that there have been a few answers in favour of the French, I'd like to make the case for the Caro-Kann defense, especially at club level.
I deliberately do not make any objective assessments, including discussions of bad bishops, tempo losses etc. (as this has been discussed before and is fruitless because both openings are objectively sound).
Also, I do not discuss personal preferences.
Rather, I would like to focus on the practical advantages of playing the Caro-Kann:
The Caro-Kann offers a much wider variety of pawn structures. This is good if you want to have interesting games and if you want to improve your understanding of chess as a whole. Also, you can play the Caro-Kann positionally or more dynamically, depending on your style preference, as there are always good options also for Black leading to very different play (e.g. 4. ..Nf6 instead of 4. ..Bf5 in the classical mainline, 3. ..c5 instead of 3. ..Bf5 in the advance and so on). You can adapt your repertoire and easily play it for a lifetime without ever getting bored.
The exchange variation of the Caro-Kann is very interesting for both sides, instead of the ultra-dull French exchange. Especially on the club level, you will face the exchange variations a lot. Black can quickly get the upper hand if White isn't careful in the Caro-Kann Exchange (compare that to the Exchange French!).
There are very few forced lines. Necessary opening theory can be heavily condensed. You can spend your time on improving other areas of your game instead of studying concrete opening variations. The Caro-Kann is very solid and often not as sharp as the French defense, therefore you won't likely be crushed in a deadly attack on your king for forgetting concrete theory. Of course, like in any opening, there are a few lines you should know really well. There are not many "tricks" or dangerous Gambits and sidelines against the Caro-Kann but there are plenty against the French. Currently, I have a lot of fun playing the Schlechter variation against French players, who almost never study this line. Even in games against very strong opposition (2200 FIDE Elo+), I have seldom faced its "refutation". One IM even deliberately did not play it "in order to avoid my preparation" even though he knew the best line, of course.
Very often, plans and ideas are easy to understand and execute in the Caro-Kann (e.g. play against the Panov-IQP or the minority attack in the exchange Carlsbad). Contrast that with statements of even 2700 Elo GMs (e.g. Svidler) that the French defense is a very hard opening to understand! The plans of adding pressure on d4 are nearly identical in the advance variation of both openings.
The Caro-Kann is a fantastic weapon to fight for a win (especially against lower-rated opposition) due to the unbalanced nature of the position. There even is a saying that "the Caro-Kann is the new Sicilian", as there are much fewer forced lines that facilitate the Sicilian becoming "dead-analysed" to a draw. Fewer forced lines mean more opportunities to outplay your opponent. If White only wants a draw, he can simplify the position more easily against the French than the Caro-Kann (e.g. by taking on d5).
All these reasons combined, together with my preference for the noble bishops explain why I would definitely choose the Caro-Kann over the French as a main weapon. My answer is partially based on the arguments given by IM Sielecki in his Chessable course.
Finally, I'd like to conclude with cold hard evidence for the higher practical value of the Caro-Kann over the French defense: statistics.
According to the lichess database, 1. ..c6 is the best-performing move out of all four major openings (1. ..e5, 1. ..c5, 1. ..e6, 1. ..c6) on amateur level across all playing strengths and time controls.
Only the Alekhine has a better score for Black among lichess amateurs. If you only consider longer time controls (rapid + classical), it is Black (!!) who wins more games than White after 1. ..c6!
On the master level, the Caro-Kann also performs better than the French defense.
I rest my case.