Jews didn't fight on a particular side. Some Jews seem to have defended cities against the Crusaders, particularly in Haifa and Jerusalem, though it doesn't seem to be a concerted effort as far as I can tell.

However, they definitely weren't on the Christian side. The Crusaders massacred the Jewish population of Jerusalem, essentially kidnapped and ransomed entire Jewish communities, and ransomed important Jewish artifacts, most notably the Aleppo Codex. Additionally, the crusades precipitated a wave of anti-Jewish violence in Europe, leading to large-scale migrations to Eastern Europe.

Keep in mind Jews were a tiny minority relative to both groups. It's easy to think of the three religions as somehow evenly weighted, but that's not really the case. The Jews were by no means a third party during the period.

tl;dr some joined Muslims in defending cities, but Jews weren't a side in the conflict per se. Jews did, however, get massacred by the Crusaders.