Not only does the form or putting names on the title matter; but more so the facts, the substance or actual occurrences, determine the ownership and the tax consequences.
For example, not putting the parents name on the title does not change that a gift was made of the funds to buy the property.
Canada does not have gift tax and US gift tax does not apply to gifts from nonresident aliens.
There is no gift tax in any event from this transaction.
If the parents are simply giving the entire purchase price then only putting you or him (or you and your fiancéé) name on the title is making the form fit the actual facts.
Depending on who the gift is being made to would make the choice for only putting you or him or you and him on the title. Who the gift is made to could have future estate tax consequence.
If the parents intend to keep some ownership (such as to later be paid back when sold) then those facts might be that one half of the price is being gifted and the other half will be owned by them (so any gain would be theirs when sold). If they keep ownership then that property would be in their estates.
Under those facts three or four names - depending on if the gift is being made to you or both you and him would be used.
As to whether it is best to have this titled only in your name, only his name, or in the name of you and your future spouse (congratulations, btw) might depend on estate tax exposure. If it is intended to keep this item out of your or his estate then not having the gift to that party and not having that name on the title may be most proper.
Income tax consequence on sale will be the same whether owned by one or both spouses. There are exclusions from gain for primary residence used two of the five years prior to sale but either spouse can be used to qualify. If the parents keep ownership there will not be exclusion on gain from their share of the home sale.
As stated, the facts behind the transaction determine the tax consequence and the form, or titling, should follow those facts.
Please ask if you need more discussion or clarification.