For one thing, the French Defense gives White less options.
In the Caro, White's serious options are the Fantasy, Exchange, Panov, Advance, and Classical. In each of those variations, Black doesn't have too many different ways to play (Bf5 or c5 in advance, Nd7 or Bf5 in Classical).
But in the French, White only has 3 options: Classical, Advance, and Tarrasch. There's plenty of choice for Black after each. For instance, after the Classical is chosen by White, Black can play the Rubenstein, the Winawer, or Nf6. And all of those variations, especially the Winawer, has innumerable sidelines, all sound, Black can hide in. As a relatively strong French player, I know of at least 8 different ways Black can play the mainline Winawer.
So, Black gets much more choice in the French.
Also it's a better opening. 
People said Caro-Kann is the "better French" due to the "French bishop" stuff. But why is French Defense played more than Caro-Kann at Super GM level?