In February, Judge Eliana Marengo told El-Alloul she would not hear her case unless she removed her hijab.
Marengo compared the Muslim headscarf to a "hat and sunglasses."
El-Alloul was in court to try to recover her car, which had been seized by Quebec's automobile insurance board.
Human rights lawyer Julius Grey filed a motion on El-Alloul's behalf.
"This case is a capsule of many of the current issues around freedom of religion," Grey said at a news conference Friday afternoon.
El-Alloul thanked fellow Quebecers and Canadians who have offered support.
"I have every right to appear before any judge, in any courtroom, with my headscarf, just as someone wearing a turban, or kippa, has," El-Alloul said.
Grey said the motion for declaratory judgment essentially asks Quebec Superior Court to issue a clear statement clarifying that people wearing religious attire can have access to courts.
El-Alloul's lawyers are still working on a formal complaint with Quebec's council of judges about Judge Marengo's conduct.