The continent would still be called North America and, if fragmented, you might have multiple nations. If looking for terms to call regions of North America that encompass multiple such nations, I don't think all would necessarily be linguistic/ethnically based, but some might. So you might have:
- Gallic-America (French-derived countries in OTL Canada)
- Either Celto-America or Nova America (countries in OTL coastal Canada)
- Anglo-America (English-derived countries in OTL colonial area and parts of Canada)
- Latin-America (Spanish-derived counties in OTL S. Cal, AZ, TX, Florida, etc)
- Native America (Native American states/nations in OTL mountain and mid west US)
- Russo-America (Russian derived states in Alaska)