A judicial official said authorities are examining several possible theories as they try to find the attacker and motive.
A gunman on a motorbike opened fire on three uniformed paratroopers at a bank machine in Montauban in southern France on Thursday, killing two and critically wounding the other.
The attack occurred not far from their barracks. The gunman appeared to be waiting for them, police said.
Four days earlier, a gunman on a motorbike shot and killed another paratrooper in Toulouse, about 50 kilometres (30 miles) away. The same calibre of weapon was used in both attacks.
A local police official in Montauban said investigators suspect a link between the two shootings.
The three men targeted yesterday served in a regiment that lost four soldiers in fighting in Afghanistan. However, the men had not served in Afghanistan.
One of those killed had served in Africa, while the other two had served in French territories overseas but not in other countries, the official said.