Yes, France is acting responsibly in stepping up aerial operations against the ISIL since the Paris attacks. I am sure they are doing everything they can and everything in their power to make sure another terrorist attack from ISIL/ISIS or any other terrorist/hate group does not happen again in the future.
By stepping up aerial operations against ISIL, France is hoping to weaken their control centers and eliminate some of the influential leaders responsible for the radicalization of young people living in countries like France. Taking the war to ISIL is justifiable seeing as ISIL seems intent on bringing terror to the streets of France.
Whether or not this is an effective solution still has yet to be proven, but it is certainly very responsible of France to try. ISIL is a huge problem and the attacks in Paris are proof of this. Something needs to be done to stop ISIl, and this is one possible solution.
War is calling war and every military action develop the feeling of vengeance. Therefore, air strike is counterproductive as it won't stop turmoil. The solution is much deeper into the roots of nowadays french society and what has been done regarding immigration policies. The past dictates what this country becomes now.