I'd say you're making a pretty big jump there.
It's just a peak season twice a week leisure route from the south of England to a little served (though sounds very nice) region of France. It looks easy for Eastern to operate as it would appear to be an extension of their existing LBA-SOU flights. Yes, SOU has a station served by London trains and for some that will be convenient, but I very much doubt anyone will try to market it as a specific London flight.