Christmas Eve December 24
This might help: http://restomontreal.ca/restaurants/f...
It has a list of restaurants that offer X-mas menus, etc.
Personally, I have only been to the The Keg (downtown) and Khyber Pass, liked both, it depends what kind of food/atmosphere you're looking for. I also heard good things about Bis and Chez Le Portugais.
The veal in cream sauce with lots of black truffle chips is very good at Bis.
Troika the Russian place downtown may be open. I ate there on Christmas Eve a long time ago. Other Russian places, different religious calendar, may be open too.
The places that are open make be packed so make reservations soon.