He is the first French foreign minister to visit Iran for 12 years and his trip comes after a landmark nuclear deal between major powers and Tehran under which Western sanctions are to be lifted in exchange for limits on Iran's nuclear programme.
Fabius took a particularly tough line with Iran ahead of the deal. He was quoted by IRNA as saying a high-ranking French economic and business delegation would visit Iran in September.
France hopes to secure business deals in Iran once international sanctions are lifted, and Fabius said last week that his hard line in the nuclear negotiations would not stand in the way of French business opportunities.
Besides Rouhani, Fabius was due to meet his Iranian counterpart Mohammad Javad Zarif, Industry Minister Mohammad Reza Nematzadeh, and Masoumeh Ebtekar, head of the Environmental Protection Agency, IRNA said.
He has said he expects to have talks "on all subjects" during the visit.
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