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"I would have to get to Dublin from Paris, but it looks like there are some cheap ways to do that."
Are award seats (in Coach) not available from DUB to CDG? The connecting flight would be included on a BAEC redemption, although you would have to be any additional fees associated with the DUB-CDG leg.
It looks like EI also offers seasonal service JFK-SNN-CDG, so depending on when you are traveling, that might also be an option.