French Defence Minister Jean-Yves Le Drian invoked article 42-7 of the EU's Lisbon Treaty that other member states have an obligation to help in the event of an attack on one of them.
Meeting in Brussels, EU defence ministers agreed to offer help and other aid to France for its military efforts in the Middle East and Africa.
"I have explained that we are prepared to open bilateral talks with France on what they then would need from Sweden and what we can provide," Swedish Defense Minister Peter Hultqvist told news agency TT.
Hultqvist said it was unclear what France might need help with. And the wording of the article gives countries flexibility in how they respond.
According to the Associated Press news agency, French Defense Minister Le Drian said EU partners could help "either by taking part in France's operations in Syria or Iraq, or by easing the load or providing support for France in other operations."
Jacob Westberg, a lecturer and researcher at the Swedish Defence University, told Radio Sweden it's unclear what form Swedish assistance to France will take.
"Sweden has said that they will commit themselves to give help fast and rapidly but," Westberg said, "exactly what kind of assistance Sweden will provide is yet unknown."
Westberg added that Sweden's promise to help France in its fight should not complicate the Nordic nation's long-standing policy of military non-alignment.
"As I see it, the question of non-alignment really isn't applicable in this context," he said. "France hasn't been attacked by another state, it has been attacked by a terrorist movement. And Sweden can't stay neutral."