"We see no indication in what President Putin says that he is going to go on the offensive," the source was quoted as saying by Reuters.
At the same time, Paris remains "extremely vigilant and alert" to the Russian military movement to prepare for any development, according to the report.
During a phone call on Saturday, Russian and French presidents discussed speculative reports alleging that Russia has plans to attack Ukraine.
"Vladimir Putin and Emmanuel Macron have discussed the situation with provocative speculations about Russia's alleged plans to 'invade' Ukraine, which have been accompanied by massive delivery of advanced arms to that country [Ukraine] as a pretext is being created for potential aggression on part of Ukrainian forces in Donbas," the Kremlin said in a statement.
Putin also drew Macron's attention to the lack of a "meaningful" response from the United States and NATO to Russian proposals on mutual security guarantees in Europe.