The man, aged in his late 30s, was intercepted on a motorway north of the French capital in the vehicle used to drive into the soldiers, the sources said, asking not to be named because they were not authorised to speak.
One source close to the case said the man had been stopped at the wheel of a BMW driving towards the northern port of Calais.
A second legal source added: "The arrested individual, born in 1980, is suspected to be the culprit" of the assault in the Levallois-Perret area of Paris at around 8:00 am (0600 GMT).
"He was driving the vehicle we were looking for and tried to flee," the source added, leading police to open fire.
Six soldiers were injured -- none seriously -- after a BMW quickly accelerated and struck them outside their barracks in a quiet street in the upmarket Levallois-Perret area.
Since 2015, France has seen a string of assaults that has left more than 230 people dead. Security forces have been repeatedly targeted by extremists inspired by the Islamic State group.
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