"Now Iran will have greater financial resources because there will be no more sanctions, we have to be very vigilant on what Iran becomes," Hollande said in his annual Bastille Day interview on Tuesday.
"Iran must show [...] on Syria that it is ready to help us to end this conflict."
Shia-Muslim-ruled Iran has supported Syrian President Bashar al-Assad against anti-government rebels, many of whom are Sunni Muslim while Assad is a member of the Alawite sect.
"A very important agreement was signed last night," Hollande commented. "The world is certainly advancing."
France hopes the deal will "allow a normalisation of relations with Iran and that a certain number of crises in which it is directly or indirectly implicated may be resolved more easily", said Fabius, who played a significant role in the talks.
The agreement allows for a gradual lifting of Western sanctions against Iran in exchange for a monitored commitment not to develop nuclear weapons.
It must now be approved by legislatures in Washington and Tehran and by the UN Security Council.
US President Barack Obama, EU foreign policy chief Federica Mogherini and Russian President Vladimir Putin all welcomed the deal, although Obama, who has to convince Congress to accept it, stressed that sanctions can be reintroduced if Iran is judged to have violated it.
Israeli Prime Minister Benjamin Netanyahu called the deal "a historic mistake for the world".
Speaking to Le Monde newspaper before the accord was signed, Fabius said it was "sufficiently robust" to calm the fears of Israel and France's Sunni allies in the Gulf, notably Saudi Arabia.