after c5 your e pawn is undermined. you don't really want to move the knight on c3 yet, if you move it back it'll clog your position, if you move it forward it'll be tempod and you'll have to retreat it again, wasting time. Which means you won't have the c3 pawn available to reinforce d4. So your pawn will end up isolated without f4. You also generally want to attack on the kingside in the french, and f4 is useful as part of that.
But I prefer the alekhine-chatard attack over Bxe7 in that position
Question: 10. f4 is not only recommended by stockfish, it is also the only book move available. So what is wrong with 10. Nf3? It develops a piece and white is now closer to castling. Stockfish thinks f4 is a lot stronger. I get that a move like f4 supports the e5 pawn. But the e5 pawn is already well defended.