"They established relations when Putin was still head of government, they had quite extensive exchanges," Kremlin spokesman Dmitry Peskov told reporters.
"They do indeed maintain quite good relations."
Peskov added that Moscow was following the French presidential primaries with "great attention."
"France is our partner, a country with which Russia maintains good relations and with which the scope of cooperation could be much larger than it is now," Peskov added.
Former prime minister Fillon, an admirer of Margaret Thatcher, pulled off a stunning upset on Sunday, knocking his former boss Nicolas Sarkozy out of the race and beating the favourite, fellow ex-premier Alain Juppe.
Business daily Vedomosti wrote Fillon was France's "pro-Russian" presidential candidate, while online news portal Gazeta.Ru said he was a "French remake of Donald Trump."
Fillon has called for closer ties with Russia and voiced support for Syrian President Bashar al-Assad's regime.
Fillon will go head-to-head with Juppe in a run-off Sunday that is widely expected to decide France's next leader after a prospective duel next year with far-right leader Marine Le Pen.
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