Paris, Lugano or Brussels?

The Brussels I Regulation and the Lugano Convention have each a territorial scope based on the same criteria. But it is not always easy to assess which instrument applies in a given dispute.

Take for instance a contract whereby a French bank assigned a claim to a French national domiciled in Switzerland. The contract contains a clause providing for the jurisdiction of French courts. The bank initiates proceedings in France. Which legal regime governs the clause?

Answer of the Paris Court of appeal: the French code of civil procedure governs, and the clause is unenforceable. Reason: the contract was not truly international, and thus only French law governed, as the only connection with a foreign country was the residence in Switzerland of one party, which was not material.  

WRONG, rules the French supreme court for private and criminal matters (Cour de cassation) in a judgment of 30 January 2013. The Lugano Convention applies, as, the court rules, the French national was domiciled in Switzerland. 

 Well, even if the French national, who happened to be the defendant, was domiciled in Switzerland, the other party was domiciled in France, and the clause provided for the jurisdiction of French courts. So why would not the Brussels regime apply?