Re: Berthiaume/Barkume;FR>QU>Detroit,MI 1790
I believe the name is pronounced something like "Bar tee ohm" with the heaviest accent on the last syllable, the next heaviest on the first syllable.
I've seen this named spelled Barcume, Barcomb, Barcume, Barkume (as my brother-in-law spells it).
When you look in Detroit, which is Wayne Co, Michigan (north of Monroe Co, which is north of Toledo, Lucas Co, Ohio - all on one of the Great Lakes) make sure to consider the two counties north of Wayne, which are Macomb and Oakland Counties.
Have you checked city directories and census yet?