MOSUL, Iraq—French special forces here have for months enlisted Iraqi soldiers to hunt and kill French nationals who have joined the senior ranks of Islamic State, according to Iraqi officers and current and former French officials.

Iraqi commanders leading the fight for Mosul said French special forces have provided to Iraqi counterterrorism troops the names and photographs of as many as 30 men identified as high-value targets. An undisclosed number of French citizens have been killed by Iraqi artillery and ground forces,...