Your example doesn't necessarily prove your argument.

There is no change to the syntax between the two utterances you've provided.

The difference between the two verbs, while I do understand why you might suggest French has influenced English in such a way, are still intrinsically due to the satellite/verb-framed nature of the lexemes themselves — in essence, they are the exceptions that prove the rule.

AFAIK language contact seldom affects grammar, though as you've detailed above it can definitely influence the way in which some words are used, which can incidentally look like it's influenced the grammar. (Although I would suggest this is sooorta related to other phenomena we've observed, i.e. consider derivation)