The 22 August attack, which gutted the centre, was at first believed to be the work of an anti-Semitic group.
Although police on Monday refused to identify the man, investigators said the man had worked on occasion as a guard at the centre. They said management had wanted to fire him.
Investigators suggested that resentment over the loss of his job could have motivated the suspect, in his 50s, to torch the eastern Paris centre out of revenge, but that explanation was not confirmed.
The man - who was placed in preventive detention for up to 48 hours - was "more or less homeless" and "mentally unstable", sources said.
The Jewish centre was destroyed in a massive blaze, and swastikas and anti-Jewish slogans such as "The world would be pure if there were no more Jews" were scrawled inside.
The incident led the French government to declare war on racism and prompted a snap visit to Paris by Israeli Foreign Minister Silvan Shalom, who urged tougher punishment in France for the perpetrators of anti-Semitic acts.
Police said the fire could have been an "inside job", but were still looking into several theories.
The police statements seemed to confirm a report in Le Figaro newspaper on Monday, which said investigators were no longer treating the fire as an anti-Semitic attack, but were looking for a mentally unstable Jewish man.
Last month, a 23-year-old woman who claimed she had been the victim of a vicious anti-Semitic assault later admitted she had made up the entire incident and was given a four-month suspended sentence for lying about it.