Candidly, I think "Yours" is just weird. Maybe even kind of creepy? Just roll with cheers and forget about it!

Therefore I stick to “Best regards” mechanically. Note that I’m French, not native in English, so I’m not mastering colloquialities. Would it be appropriate to be more relaxed?

"Veuillez agréer, Monsieur, l'expression de mes sentiments les plus agréeables"

(Please be so good as to accept, Sir, the expression of my warmest feelings)

Well, that's what they told me at school - they were trying to teach me how to write business letters. It has always cracked me up.

/me not French.

I once wrote both an employee’s resignation and my acceptance for the conditions of it (on his request for both, he’s non-native), and it was awkward to try to find a valediction that doesn’t put him as inferior.

Language is a treasure.

You can have a fairly good command of a foreign language, but still fail at communicating. You also need to understand cultural conventions and customs, and for that there's no substitute for living there.

I've never written a formal letter in French. I don't know why they sent me to school at all, really.

/me went to a French school, in France, for two years. When I was 4. I know French nursery rhymes.

That would actually be somewhat familiar for a formal letter. You probably wouldn’t use "les plus agréable" here but rather "respectueux" or "les meilleurs". People just copy and paste them from the internet nowadays when they need to use one.

I didn't know that actual French people had to google to find the right terminology for a formal sign-off; that just adds to the hilarity.

I never had a sig - not for email, not for Usenet. At one time I just signed off with my name; nowadays I make do with a bare carriage-return. I figure people will be able to work out when they've got to the end.