Gibson-Park reported he is suffering from hamstring tightness after the 50-17 demolition of Italy at the Aviva Stadium on Sunday (AEDT).
Cooney was left out for that match in Dublin after being on the bench for the defeat to England in February before the tournament was halted due to the coronavirus pandemic.
The Ulster scrum-half has been drafted in by Andy Farrell ahead of a showdown with Les Bleus in Paris which Ireland start knowing a bonus-point win would secure the title.
Wing Keith Earls is finishing his rehabilitation programme from a back injury and a decision over whether he can face France will be made in the coming days.
Centre Garry Ringrose is out for up to six weeks after suffering a broken jaw in the hammering of the Azzurri.
England trails Ireland by a point but is the favourite to be crowned champion as it faces Italy in Rome.