The march was held in memory of the 17 who died during the terror attacks in the French capital last week.
As well as 10 journalists, four Jewish people perished in a siege by Islamic militants at a Kosher supermarket.
Speaking to one woman in the crowd who said she believed the issue of Jewish persecution dated “back to the days of the 1930s in Europe”, he replied: “Many critics though of Israel’s policy would suggest that the Palestinians suffer hugely at Jewish hands as well.”
Video Clip Of Interview
“We can’t do an amalgym,” she responded, shaking her head.
To which Willcox said: “You understand everything is seen from different perspectives.”
The woman, who has since been named online as Chava, was reported by the MailOnline to be an Israeli national who is the daughter of Polish Holocaust survivors.
Willcox has since expressed his regret over the remarks, tweeting:
In a statement, a BBC spokesperson said: “Tim Willcox has apologised for what he accepts was a poorly phrased question during an in-depth live interview with two friends, one Jewish and of Israeli birth, the other of Algerian Muslim heritage, where they discussed a wide range of issues affecting both the Muslim and Jewish communities in France.