At least one person has died and five are injured. According to BFMTV, the condition is critical for two of them.
The incident is said to have occurred during the night towards Saturday, when a car drove into several people at a bar.
The whole thing was preceded by an exchange of words outside the bar, says prosecutor Rémi Coutin to the news agency AFP. After the quarrel, a person is said to have gone and fetched a car and "deliberately backed into a crowd" at high speed.
Three people have been arrested.
Évreux is located in northwestern France, just under ten miles west of Paris.
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