The French are an intensely proud nation and can be very determined in something like this. They also have a fine engineering & technology tradition and in previous air accidents where French nationals were involved (eg Flash Airlines 604 - Egypt) have gone to extreme lengths to recover the FDR & CVR. In that case they had a Navy salvage ship and ROV on site and the recorders recovered within two weeks - pretty impressive, although the depth was 'only' 1000m.
If the debris field is found, they will be on the case faster than you can say 'Jacques Cousteau' and if there is even a remote chance the DRs can be recovered, they will get them.