Gignac, who has scored three goals in three games to help Marseille enjoy a perfect start to the season, had not made France squad since the 2010 World Cup.
The 27-year-old, who has played 16 times for France, rediscovered his scoring touch last season with 13 league goals after two dismal campaigns under former Marseille coach Deschamps in which the pair endured a difficult relationship.
"My point is to call players who are efficient and who can bring something to the squad," Deschamps told reporters.
"We had had a troubled relationship in Marseille but then I had to field him and time has gone by. We have talked about this and we don't have anymore problems from this points of view," he added.
Although France are used to playing with only one striker, Deschamps hinted Gignac could feature in one of the games despite competition from Karim Benzema and Olivier Giroud.
France have been not scored in their last four matches and Benzema has not found the net since a friendly against Estonia before the 2012 European Championship.
"Regarding what (Gignac) has achieved with his club and the needs that are ours, he can have a role to play," Deschamps said.
Midfielders Paul Pogba and Blaise Matuidi, who are suspended for the Georgia game on September 6, returned to the squad.
France are second in their qualifying group, one point behind world champions Spain with three matches left.
They host Finland for the final game next month.
Goalkeepers: Mickael Landreau (Bastia), Hugo Lloris (Tottenham Hotspur), Steve Mandanda (Olympique Marseille)
Defenders: Eric Abidal (Monaco), Gael Clichy (Manchester City), Mathieu Debuchy (Newcastle United), Patrice Evra (Manchester United), Laurent Koscielny (Arsenal), Eliaquim Mangala (Porto), Adil Rami (Valencia), Bacary Sagna (Arsenal)
Midfielders: Etienne Capoue (Tottenham), Clement Grenier (Olympique Lyonnais), Josuha Guilavogui (St Etienne), Geoffrey Kondogbia (Sevilla), Blaise Matuidi (Paris St Germain), Paul Pogba (Juventus), Moussa Sissoko (Newcastle United)
Forwards: Karim Benzema (Real Madrid), Andre-Pierre Gignac (Marseille) Olivier Giroud