"Mayday" is an emergency procedure word used as a distress signal in voice procedure radio communications in English.
What would be the equivalent in French?
Mayday is phonetically transcribing the ungrammatical French "M'aidez !".
This expression is never used as is in spoken French. Idiomatic ones are "Aidez moi !", "A l'aide !" or "Au secours !".
Mayday is rarely heard either in French radio communication outside a potentially international context (planes/boats). For ground communications, one might prefer instead "Urgent ! Urgent ! Urgent !" to interrupt any ongoing communication.
Mayday was coined by Frederick Stanley Mockford from the correct French "Venez m'aider !".
This is an international distress signal; it is also "Mayday mayday mayday" in France, see mayday on the French wikipedia.
MAYDAY is arguably more French than English, but MAYDAY is certainly the standard expression for this condition in the English-speaking world, which, by international agreement, includes aviation.
This agreement does not preclude local languages from being used, but during critical phases of flight, standardized terms are highly recommended.
...as deemed by the International Civil Aviation Organization (ICAO), English is the official language of aviation.
Many non-native English speaking pilots and air traffic controllers learn English during their flight training and use it in a highly practical level while safely operating an aircraft...