English resembles the Latin ancestor more than the French intermediary.
Late Latin falco, with stem falcon-, led to Anglo-French faucon. English borrowed the word in Middle English, which had forms including faucoun and falcon.
The dictionary qualifies the deeper derivation as probable. It is outside the scored route; the Middle English variants are not ordered against each other.
Source
Merriam-Webster: falconWord History supplies the borrowing route and alternative Middle English forms, while qualifying the deeper origin.