[checkyoursudo]

Specifically, it's an abbreviation of the French messieurs, which is just multiple misters. Maybe it's more formal now, but it was ordinary and frequently used in the past in both French and English writing. (Obviously, still quite commonly used in, um, French today.)

E.g., English https://books.google.com/ngrams/graph?content=messrs&case_in...

French https://books.google.com/ngrams/graph?content=messrs&case_in...

[frutiger]

In particular, compare: “mon sieur” vs. “mes sieurs”.

[checkyoursudo]

Indeed

[Milner08]

English words of French origin are normally considered formal. Back when the French invaded England the rich spoke French, while the poor spoke Anglo Saxon. The words mutated and changed but words of French origin are now formal because of this.

[baud147258]

As a French, it feels weird to learn something about my language on an English site :|. I don't remember seeing it written in French. Or I saw it, understood the meaning and forgot.

[lloeki]

That's because it's largely unused nowadays, the current abbreviation being MM. (which doubles the M. – not Mr! – abbreviation for monsieur).

[GuiA]

You’ve probably heard it without noticing - eg “Mesdames et messieurs” (ladies and gentlemen) is still in common use.