Same phrases in English - lâcher = let one go/let one off/drop one/let one rip/let one drop.... (see google for a list of synonyms).
But (for the cheese link) it is possible to say "Stilton?", very sarcastically and sniffing the air.
Could a French person say "Reblochon?" in the same way?
This is not a well-known set phrase but a little joke which would depend on others understanding what you meant. "Munster?" also qualifies and "Tome des Pyrenées?"
Actually, "cut the cheese" is in google but I've never heard it used like that in southern England - Canadian? American?
Not totally off topic, it is good, if informal, AE to say "I cut a fart" for "I farted". To a BE speaker like me, that seemed mad the first time I heard it. But it is usually obvious, quite soon, what it means.