Levallois-Perret Mayor Patrick Balkany said a BMW parked in an alley drove into the soldiers as they left their barracks to go on patrol duty.
Man carrying knife arrested at Eiffel Tower
Police said two of the six were seriously injured. Speaking to broadcaster BFM TV, Balkany said that what he called a "disgusting" act of aggression was "without any doubt" premeditated.
France's police department said in a message on Twitter that a search for the vehicle was under way.
France remains on maximum alert after a string of attacks in which militants have killed more than 230 people over the past two years.
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