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Americans do not need visas to enter Canada. However, he have to demonstrate at the border that he intends to return to America with in the timeline of his visit allowance (generally 6 months I believe). He certainly cannot move to Canada with his things and stay there without applying for a visa.
 
I'd like to add to that that there is no fiancee visa in Canada. What other people generally do is cross the border and in case someone asks, say they are coming to visit bf or gf in Canada. During their visit, they just happen to get married in which case they may apply to extend their visitor status and apply for sponsorship.

Tell your fiancee to ask for the passport to be stamped on entry to Canada because that way, they can prove when they entered and can ask to extend their visitor status more easily based on that. Tell your fiancee not to show up with all their belongings in a u-haul at the border or mention any plans to stay longer than 6 months because they may be turned away and possibly even banned from Canada for a while.