Is it possible that a court of one jurisdiction would apply the laws
of another jurisdiction? For example could a case heard in France (by
a French court) apply the laws of the US? If no, then what is the
point of such clauses?
Yes. This can be done and the example you provide could happen.
This is done in civil cases, but not in criminal cases. The other main exception is that a court will not apply another jurisdiction's tax laws, although this is less absolute and the other jurisdiction's tax laws may still be considered as relevant to a civil dispute, so long as they are not enforced.
For example, I have litigated a case where the events took place in France in a U.S. Court where the court had jurisdiction over the parties and the relevant choice of law rules pointed to French law.
The overarching principle of that the law of the place with the most significant connection to the legal issue decided applies. But there are many subsidiary rules that provide clarity in some areas (although the clarity was reduced with the effect of making forum law apply more often, in the 1960s-1980s after a previous regime of more black and white rules).
A clause like this is generally effective if it the parties have any connection to the forum chosen. It is a close cousin, although not nearly so strongly preferred in the law, of an arbitration clause.
Also do such clauses go by other names than "attornment" clauses? This
article points out such a name is specific to Canada.
Yes. In the U.S. an "attornment" clause is a provision that requires a party to a contract to affirmatively declare upon notice from the other party if the attorning party claims that the other party is in breach of the contract or has unfulfilled obligations (with the attorning party waiving any claims for breach of contract not identified at that time). An "attornment" clause is normally found in a lease or secured promissory note and facilitates the transfer of the leased property or secured debt in a way that the new owner can know that there is no risk that it is already in default apart from the transferor's representation. Otherwise, the aggrieved party wouldn't have to mention anything until the statute of limitations arrived.
All of the meanings, including the Canadian one, go back to the notion of affirming the existence of certain rights in advance of a dispute arising between the parties.
This Agreement shall be construed, interpreted and enforced in
accordance with, and the rights of the Parties shall be governed by,
the laws of the Province of Québec and the federal laws of Canada
applicable therein (excluding any conflict of law rule or principle of
such laws that might refer such interpretation or enforcement to the
laws of another jurisdiction).
The language above is a choice of law clause.
The Parties hereby irrevocably attorn to the exclusive jurisdiction of
the courts of the Province of Québec, judicial District of Montreal,
with respect to any matters arising pursuant hereto.
The language above is a choice of forum clause, a.k.a. choice of jurisdiction clause, a.k.a. choice of venue clause.