PARIS — Ten young Muslim men, bored by a mundane life in France and haunted by a “feeling of uselessness,” as one put it, were seduced by a leading Islamic State recruiter in Europe in 2013. Within months, they were in Syria under the watchful eyes of hooded, Kalashnikov-wielding militants, doing push-ups, fiddling with weapons and imbibing the ideology.

But the harsh regimen, most have since told investigators, was not to their liking, and it was not long before they hastened back to their families in the Strasbourg area, where they were almost immediately picked up by the French authorities.

What to do with hundreds, perhaps thousands, of such young men in Europe is now among the biggest challenges facing governments and security services.

After the Paris and Brussels terrorist attacks, which were carried out in part by Europeans who had spent time in Syria with the Islamic State, France and other countries are grappling with how far to go in tightening laws to prosecute, monitor and restrict the movements of returnees.