The visit, scheduled for June 24-25, will be Tsvangirai’s first overseas trip as prime minister, an official said on Friday.
Idrac issued the invitation during her visit to Zimbabwe, the first by a French minister since the power-sharing government was formed in February.
"I hope the mission will be successful when you come (to France) next month," Idrac told Tsvangirai at a press conference.
"We are very impressed by the job you have done in the first 100 days," she added.
"My feeling is that should you not succeed, it will be the collapse of your country."
Tsvangirai said the formation of the power-sharing government was the only option for Zimbabwe as the country faced worsening political and economic crises.
"The challenge to the international community is how they react after the signing of the political agreement," Tsvangirai said.
He also commended the International Monetary Fund as its technical co-operation team completed its mission on Friday.
"The IMF has been very helpful," Tsvangirai said. "We are working closely to monitor their recommendations."