Hi Tom,
I haven't had much success tracing John Peter Levesque back to QC. I do not speak french and the early records are in French. I did find several years ago a death record in early Caribou for an Amab Levesque who lived to be quite old who came from the same city as John Peter. Maybe a connection. According to the death record, Amab died March 15, 1915 in Caribou at the aged of 95. He previously resided in Connor, ME. He was born in Rivière-du-Loup. I've never heard that John Peter might have Indian ancestors. I imagine it's certainly possible.
Dale