European Parliament president Martin Schulz said he had referred the matter to the French authorities "given the seriousness of the reported facts and their possible criminal implications".
Mr Schulz said he referred the "regrettable" incident to the authorities after a recommendation from the European Parliament's advisory committee on conduct.
He told the parliament:
(The committee) concluded that the versions of the facts given by the two members involved diverged substantially and the facts seem to have happened in the absence of direct witnesses.
He stood by his claim that he had "received a blow" from Ukip MEP Mr Hookem during the altercation and revealed he had made a police complaint about the incident.
Mr Hookem has denied hitting the North West MEP and the fallout from the incident has continued with claims that Mr Woolfe had received warnings about "inappropriate behaviour" from senior party figures.
The new Ukip leader will be announced on November 28, with nominations to replace Ms James closing on October 31.
Among the contenders are Suzanne Evans, Paul Nuttall and Raheem Kassam.