Gourcuff was sacked earlier this week despite managing four wins on the trot in all competitions for Rennes, with former Ivory Coast chief Lamouchi replacing him.
Lamouchi has signed a two-year deal and he admits he has a lot of respect for his predecessor.
"I'm coming into a bit of a special situation," he said. "I'm replacing someone for whom I have a lot of esteem and respect as a man and as a professional.
"I'm inheriting a team that's winning, which is full of confidence, which is young but has potential.
"We going to try to get to the heart of the matter, but the project is simple: get the most from the players that we have, give them enthusiasm and the ambition to be able to have fun together and keep the run going. I'm really fortunate to be here."
Lamouchi's first game in charge is against Strasbourg on November 18.