"A shootout this evening has left one dead and 4 injured in a Chicha bar on rue Popincourt #Paris11. No element at this stage makes it possible to know the motivations behind this barbaric act," Vauglin said on Twitter on Monday night.
He added that one of the two attackers has been caught, while the second suspect is on the run.
BFMTV said citing police sources that the shooting took place at 21:35 local time (19:35 GMT) on Monday, when two individuals got out of a vehicle and fired at two other people who were seated on the bar terrace.
According to French media reports, the shooting was likely a settlement of personal accounts.