The most significant ones I've come across are "filet". Americans say "fill-aye", Brits say "fill-et". Apparently the origin is Middle English and Old French. Why do Americans pronounce and spell it in the French way?

Same thing with dropping the "h" at the front of "herb." Americans do this; Brits don't; word comes from Middle English via Middle French (herba or herbe).

And yet I've been told that British people began to adopt spellings with the letter u and doubling up on the letter l in order to seem more French.

Why do Americans pronounce words in the French way? Is this because some parts of the US were French territories? Have those pronunciations and spellings always been present, or were they adopted late in the day to make things seem more French (as in England)?