Can I sidestep a red line spelling checker in words other than English?
Language and Region doesn't really have anything to do with spelling in MacOS.  Instead go to System Preferences/Keyboard/Text/Spelling and set the language there, plus maybe in Edit > Spelling and Grammar > Show Spelling and Grammar if necessary.

Some non-Apple apps like Word have their own independent spelling settings.

If you need to do both languages at once, you can try the Automatic setting in Spelling, after going to the Setup item and checking the boxes for just those two languages.  How well this works in practice you will have to determine by testing with your particular text.

A better solution would be to use a more advanced app like Pages or Word, where you should be able to set the language of individual text runs so that the right spell check is used for each.

I think it may work better in iOS.  If you have such a device, activate the French and English keyboards and dictionaries.  My initial test indicates it handles a text like yours correctly.