Air France Frequence Plus - Air France Luggage question

We want to book tickets for next summer for a JFK-CDG-BCN-JFK flight. The cheapest price seems to be with Air France for the first two legs and Delta for the return from BCN. I know that Air France and Delta have different international baggage allowances, my question is to the CDG-BCN flight. IF I book the whole flight on Air France (the Delta leg is also an Air France code share flight) I know I'll get 2 pieces per passenger included on each leg. If I book it as the two separate airlines, will the CDG-BCN flight be treated as a continuation of the international flight with an open jaw, or is it an inter-European flight? That's the big question, because the baggage allowances aren't as generous with inter-European flights.