PARIS—France launched airstrikes against Islamic State in Syria, responding to terror attacks on its capital, as investigators pieced together a chilling picture of Europe’s security: a continent at a loss to foil, let alone detect, such a coordinated plot.

As a stunned France mourned 129 dead, authorities were racing Sunday to find one suspect believed to have been involved. Officials began retracing the paths of the assailants, who they believe carried out the massacre on behalf of the extremist group.

One of them, they said, appeared to have spent time in Syria in 2013 and 2014. Another, they suspect, came into France possibly posing as a refugee. At least several of them had moved undetected by both the French and Belgian governments, using an operating base just 50 miles off France’s border, in Brussels.

“The attacks were planned abroad, and mobilized a team operating from Belgium, which may have received help from France,” French Interior Minister Bernard Cazeneuve said.

As of late Sunday, an international manhunt was under way for Abdeslam Salah, a 26-year-old man born in Belgium, whose brother was among the seven suicide bombers who wreaked havoc at a sports arena, a concert hall and through the streets of Paris late Friday.