When did Lutetia begin to be known as Paris?

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Paris; Eiffel Tower — Paris View of the Paris skyline from Montparnasse.

The settlement originally known as Lutetia began to be referred to as Paris from the early 4th century CE.1

Following a series of barbarian invasions that began in the late 2nd century, the town on the left bank of the Seine was destroyed by the mid-3rd century. In response, the inhabitants retreated to the Île de la Cité, where they constructed a thick stone wall for protection, and the site subsequently became known as Paris.1