Police sources told the broadcaster that the suspect could be seen on video footage of the incident calling Mr Finkielkraut a “Zionist”, a “piece of sh*t”, and telling him “France belongs to us”.
The attack on Mr Finkielkraut last Saturday was followed on Tuesday morning by the discovery of a desecrated Jewish cemetery in Quatzenheim, in the northeastern region of Alsace.
Swastikas and German slogans were graffitied on some headstones, while others were smashed off their pedestals. In all, 96 graves were daubed in blue and yellow paint.
President Emmanuel Macron visited the cemetery the same day and promised to take more action on hate crimes.
The broadcaster France 3 said it was forced to abandon a live Facebook feed showing footage of his visit to the Quatzenheim cemetery because of an onslaught of antisemitic comments.
“We are talking about explicit death threats, comments that were openly anti-Semitic and racist, including 'Heil Hitler', 'dirty Jew' or 'dirty Jews', comments that were addressed at Emmanuel Macron and representatives of the Jewish community,” the channel said in a statement to Reuters explaining its decision.
“Within minutes, the number of vile and illegal comments had gone well beyond our capacity to moderate them,” it explained. “We refuse to traffic in hatred.”
Later on Tuesday thousands attended a demonstration at the Place de la République in Paris under the slogan “That’s Enough”.
They were joined by figures from across the political spectrum, including Prime Minister Edouard Philippe and former Presidents François Hollande and Nicolas Sarkozy.