Mayday’s roots are in French, while May Day’s roots go back to pagan spring celebrations.
The distress call “mayday” was invented in 1921 at the Croydon airport in London. Much of the traffic to Croydon airport at the time was from France and so “mayday” was chosen because it sounded like the French “m’aider” (“help me”).
Mayday the distress call has nothing to do with May Day, the May 1st pagan spring holiday celebrated in various fashions since the Ancient Romans. Eventually, in an attempt to stop paganism, May 1st was appropriated by the Catholic Church and dedicated to Mary.
In the early 20th century May Day also became the International Workers’ Day, celebrating labor & workers around the world (except in the United States, where it’s called Labor Day and celebrated the first Monday in September).