"The expectations of the international community with regard to Iran are significant, especially about its nuclear programme and its involvement in Syria, " French Foreign Minister Laurent Fabius said in a statement.
"We are ready to work on them with the new president," he added as he praised the "Iranian people's resolute desire for democracy".
Rowhani, 64, was declared Iran's new president in an outright election victory, to replace Mahmoud Ahmadinejad.
He is a former top nuclear negotiator who has championed more constructive engagement with world powers.
Tehran agreed to suspend its controversial enrichment of uranium when Rowhani was Iran's nuclear negotiator under reformist ex-president Mohammad Khatami.
The programme was restarted two years later when Ahmadinejad became president.
Iran has been at loggerheads with world powers over its nuclear drive, which the West suspects is aimed at developing an atomic weapon capability.
Tehran denies the charge, but the sanctions imposed over the stand-off have isolated it internationally.