Three French soldiers were stabbed while patrolling a Jewish community centre in Nice on Tuesday.
The attacker, who has been named as Moussa Coulibaly, "rushed at the throat of one of the soldiers", Christian Estrosi, the Mayor of Nice, told reporters.
The soldier escaped with minor injuries to his face, he said. Coulibaly, who was using an eight-inch blade, then lashed out at two other guards. One was also injured in the face; the other in the arm.
The assailant was arrested after trying to flee on foot. On Wednesday, a second man was arrested in connection with the stabbing.
The Jewish community centre is in the centre of Nice and home to an Israeli association and a Jewish radio station.
The attacker shares his surname with Amedy Coulibaly, who murdered four Jews at Parisian kosher supermarket Hyper Cacher last month.
French authorities said it was unclear whether the two were related or whether they had known each other.
Newspaper Le Monde said that Moussa Coulibaly had sparked the attention of the police after he flew to Turkey on January 28. Turkey has been used as a gateway for people seeking to join jihadi groups in Syria. But the Turkish authorities sent him back to France at the request of French intelligence officials.
President François Hollande issued a statement condemning the Nice attack "with the greatest firmness".
Mr Hollande said officials would "shed light on the motivations and circumstances of this criminal act".
France has been on high alert since the January attacks in Paris. More than 10,000 soldiers have been deployed around the country to protect sensitive locations, including major shopping areas, synagogues, mosques and transit hubs.
The Nice attack coincided with the emergence of a video by Islamic State inciting French jihadis to carry out further terrorist acts.