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All that really matters is that the carriers involved have interline agreements. If so, they can be ticketed together.
By definition all airlines in the same alliance have interline agreements with each other.
Multiple airlines can be combined on a single ticket. Such connections are protected.
However if combining airlines I would only book such a ticket directly with one of those airlines, not through a third party.
You can also take a TGV from CDG to Bayonne with a change of train other than Paris, which is much easier as going through Paris means arriving at Gare de l’Est and taking a taxi across the city to Gare Montparnasse.
Taking a TGV from CDG requires a change of trains, but will be more convenient than taking the RER into Paris and then making your way to Gare Montparnasse with luggage. Paris has nearly a dozen long distance train stations and they are not easy to connect between.
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