The move follows a complaint lodged last month by an anti-racism organisation that numerous messages posted on the site had breached French law prohibiting incitement to racial hatred.
Video courtesy of jn1.tv
The police probe, which is still in a preliminary phase, will focus on one specific message with a view to pressing charges punishable by up to a year in prison, judicial sources said.
France's Union of Jewish Students (UEJF) has been pressing Twitter to exercise tighter control of what appears on its site following a wave of anti-Semitic messages posted under the hashtag #unbonjuif (#agoodjew).
Examples included "#agoodjew is a dead Jew" and other offensive tweets were subsequently posted under #unjuifmort (#adeadjew).
The UEJF on Tuesday began a legal action aimed at forcing Twitter to identify the authors of some of the posts. A hearing on the application has been scheduled for January 8.
Twitter has refused to comment on the row, re-directing enquiries to its terms of service which state that it does not mediate content but may suspend accounts deemed to be producing illegal content.
In October, the site suspended the account of a neo-Nazi group in Germany following a request from the government in Berlin. It was the first time Twitter had acted on a request of that nature from a government.