The biggest difference is that where the move 3.e5 cramps Black in the French, it has no cramping value in the Caro-Kann. Black plays 3...Bf5. At one time the move 3.e5 was even considered weak because of continuations like 4.Bd3 Bxd3 5.Qxd3 e6, when Black has an easy game.
Later the variation 4.Nc3 e6 5.g4 Bg6 6.Nge2 was discovered. White has threats against the Bishop which is exposed precisely because it is outside the Black Pawn chain. Some typical ideas are 6...c5 7.h4 or 7.Be3; 6...Ne7 7.Nf4; and 6...f6 7.Nf4 or 7.h4. The resulting positions are filled with unusual Pawn thrusts, and often both players can safely neglect castling. Its main advantage is psychological: Black seeks a quiet game, but is forced to play complex positions.
White has quieter continuations with slower buildups like 4.Nf3 e6 5.Be2, where Black must eventually play ...c5 to stay in the game. This is possible immediately with 5...c5, although Black can prepare it with 5...Nd7 or 5...Ne7. The move 6.O-O is good after any of these.
If Black doesn't want to allow the complications resulting from 4.Nc3, the move 3...c5 followed by 4.dxc5 e6, steers into a French Defense where White has an extra tempo.
