Paris, however, quickly dismissed the allegation and said that the jet involved in the incident was actually Swiss.
The ministry in Moscow said in a statement that it had summoned France's ambassador Jean-Maurice Ripert to "give an explanation" of the incident.
"A plane of the French airforce flew dangerously close to a jet with a Russian parliamentary delegation headed by the Russian State Duma speaker Sergei Naryshkin," the statement said, adding the officials were travelling to a meeting of the Inter-Parliamentary Union in Geneva.
France's foreign ministry rebuffed the Russian claim, saying that "it was a Swiss plane, an F18, and no French military plane is involved."
Naryshkin's spokeswoman Yevgenia Chugunova told AFP that the warplane flew so close that members of the delegation could take a picture.
"I can confirm that this incident involving a French military plane happened this morning," she said. "We saw it very close."
Another member of the delegation, Sergei Gavrilov, told TASS news agency that the approach took place "at the altitude of 3,700 metres (12,100 feet) above the Swiss border" and called it an "unfriendly act by NATO".
