The attack took place shortly after nightfall in the city's 10th arrondissement, home to a large South Asian community.
Diners watched in horror as two assailants stormed the restaurant and struck the 35-year-old man of Sri Lankan origin in the head and arm before fleeing.
The man was rushed to hospital in a critical condition.
A source close to the probe said on Tuesday that investigators suspected a settling of scores in the Sri Lankan community.
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