Some students said he was a "freak" who called his lover "Josephine" (Napoleon's first wife) and asked to be addressed as "Sire".
His relationship with Yeshchenko was an open secret, he said.
He has reportedly been detained in hospital where he is being treated for hypothermia.
They had also co-authored a number of historical papers together at St Petersburg State University, where Sokolov was a professor in the history department.
Both he and Yeschenko enjoyed wearing period costumes, with Sokolov frequently dressing up as Napoleon.
A historical re-enactor, Mr Sokolov has often appeared in uniforms of the Napoleonic era, and has worked as a consultant on historical reproductions for film and TV.
"I can not get my head around it", historian Ilya Kudryashov told AFP.
On Thursday, Sokolov allegedly killed his purported lover in an act of jealous rage, according to unconfirmed claims, cited by the media.
Vasily Kunin, who studied with the victim, blamed university management.
"There was a policy of hushing things up".
It added that law enforcement officials were also looking into media reports that Mr Sokolov beat some of his students.
On Twitter, screenwriter Andrew Ryvkin said Sokolov was one of his lecturers, describing the Saint Petersburg-based university as a place where "alcoholics" and "anti-Semites" felt at ease.
Sokolov was president of the Russian Association of Military History and is now a member of the body's scientific council.
A spokeswoman for the Grand Chancery of the Legion of Honour, speaking to AFP, indicated that Sokolov might be stripped of his award.
The organisation immediately sought to distance itself from the controversy.
"We learn with horror. the atrocious crime of which Oleg Sokolov is guilty.", it said.
ISSEP was founded by Marine Le Pen's niece, Marion Marechal.