"Let us forget the resentment," Rouhani said, calling for both countries to take advantage of the "positive atmosphere" following the removal of sanctions over the Islamic Republic's nuclear programme.
"We are ready to turn the page" and establish a "new relationship between our countries", Rouhani told a meeting of business leaders.
French Prime Minister Manuel Valls responded that "Iran can count on France".
"France is ready to use its companies, its engineers, its technicians and its many resources to help to modernise your country," Valls said.
Rouhani was welcomed to Paris with military honours and national anthems on the second leg of a trip signalling Iran's rapprochement with Europe since sanctions were lifted.
The real business of the visit will come when Rouhani officially signals Iran's intention to buy more than 100 passenger planes from European aircraft maker Airbus.
French carmaker Peugeot said it will return to the Iranian market in a five-year deal worth 400 million euros ($436 million) that was announced Thursday. Peugeot will produce 200,000 cars a year in a joint venture with local manufacturer Iran Khodro, according to a statement.
The French carmaker was forced to pull out of Iran in 2012 as sanctions began to bite. In another potential bonanza for France, the head of French oil giant Total said his firm would sign a deal to buy Iranian crude.
Although the French state is rolling out the red carpet for Rouhani, the Iranian opposition will hold a human rights demonstration and Jewish groups also intend to protest in Paris.
Rouhani is to hold talks with President Francois Hollande which are expected to include discussions on Iran's role in Syria, where it is backing President Bashar al-Assad in a war that has killed 260,000 people.
Talks are due to begin Friday in Geneva to take tentative steps towards ending the conflict.