PARIS — France eased its gun rules on Wednesday to allow off-duty police officers to carry their sidearms even if the nation is not in a state of emergency. The move was a response to an attack on Monday in which an Islamic State assailant fatally stabbed a policeman and his companion at their home while their child was there.

The eased rules, welcomed by France’s police unions, came as the authorities in Belgium alerted police that more attacks appeared to be in advanced planning stages and could be imminent.

A group of extremists have left Syria and divided into smaller groups headed for Belgium and France, the warning said.

The information was reported by a Belgian newspaper, La Dernière Heure, which said police had received an alert that “combatants left Syria about a week and a half ago in order to reach Europe via Turkey and Greece, by boat, without passports.”