Les Bleus trailed inside two minutes after Paul Pogba fouled Shane Long and Robbie Brady clipped home the penalty off the post.
Ireland closed the first half with desperate defending, but France attacked with more purpose and intelligence in the second half.
They were rewarded with a stunning brace for Antoine Griezmann, the Atletico Madrid star, and it could have been more after Shane Duffy was sent off for a professional foul.
