PARIS—The French government announced new measures on Friday to curb Islamic radicalization in schools and prisons as the country faces the return of hundreds of nationals who joined Islamic State militants in Syria and Iraq.

French Prime Minister Édouard Philippe said the government planned to open 1,500 new spots in dedicated, high-security wards for hardened radicals in several prisons across the country, including 450 before the end of the year. Teachers will also be trained to identify radicalized teenagers and shutting...