The armed forces said on Thursday that a Swedish naval ship observed the suspected drone during a patrol in the Öresund Strait, which divides Sweden from Denmark.
They said that unspecified countermeasures were taken to disrupt the drone, and that contact with it was then lost.
The French nuclear-powered aircraft carrier Charles de Gaulle is in the southern Swedish city of Malmö this week as part of regular NATO exercise activities.
Malmö is located on the Öresund, opposite Denmark's capital, Copenhagen.
French military spokesperson Guillaume Vernet told The Associated Press that the drone was detected on Wednesday and handled by Swedish forces integrated into a security system around the carrier.
He said on Friday that the drone was more than 10 kilometres from the Charles de Gaulle.
"This system showed it is robust, and this event had no impact on the activity of the aircraft carrier battle group," Vernet said.
Swedish Defence Minister Pål Jonson told public broadcaster SVT on Thursday evening that the suspected violation of Swedish airspace by a drone happened in connection with a Russian military ship being in Swedish territorial waters.
Asked what country he thinks the drone belongs to, he replied: "Probably Russia."
The Russian ship continued into the Baltic Sea, and Swedish authorities have been in close contact with Denmark about the incident, Jonson said. The armed forces said that no further drones were observed.
Swedish Prime Minister Ulf Kristersson said during a visit to the French ship on Friday that "everything implies that it is a Russian violation of Swedish airspace," but he wouldn't go into detail.
He added that "it is serious and maybe not surprising," as Russia dislikes western exercises and the west dislikes Moscow's actions.
French Foreign Minister Jean-Noël Barrot, who also visited the Charles de Gaulle, emphasised that the security of the aircraft carrier wasn't threatened.
"If indeed ... there is a potential Russian origin for this incident, it would be a ridiculous provocation," he said.
He said that he had no information of his own on the source of the drone.
Kremlin spokesperson Dmitry Peskov said he didn't know about the incident.
Asked by reporters about Swedish officials linking the drone to the Russian ship, Peskov said that "it's quite absurd" to claim that the drone was Russian just because a Russian ship was nearby.
Western officials say Russia is masterminding a campaign of sabotage and disruption across Europe.
An Associated Press database has documented well over 100 incidents.
Not all of them are public and it can sometimes take officials months to establish a link to Moscow.
While officials say the campaign — waged since Russia launched an all-out war against Ukraine in 2022 — aims to deprive Kyiv of support, they believe Moscow is also trying to identify Europe's weak spots and divert law enforcement resources.
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