Gatineau is mostly French, although while English is spoken, unless it’s Montréal, Québec City or maybe Trois-Rivières, you’ll have to learn some French to get by, so I would consider that…not a mastery of the entire language, but some basics; you’ll learn the language fast enough if you live there anyways.
If you can manage the trip from Québec to Ontario twice a day, it’s entirely possible, but that might depend where in Ontario you work.
Not wanting to discourage you, but I personally wouldn’t do it. If you don’t have a car, you’ll have to get to Ottawa by bus and then transfer to wherever you work. Not sure entirely about their bus routes, so that’s another step for you, find out about it so you know exactly what buses to take to get to and from work.
But, for sure they have regular public transportation between the two provinces.
As for the steps well, look for a place in Gatineau and go by the normal procedures, but reserve some spare time to drive back and forth to visit places several times, meet up with the landlord to settle things and all, or do it by phone or e-mail.
If you already have a job in Ontario, some people might get iffy about it, but they have no reason not to rent you an apartment.
You can also look up information online to check out places for rent in Gatineau, and I’m pretty sure somewhere in Ontario they sell “Le Journal de Montréal” which is Québec’s main newspaper. They got places for rent for pretty much the whole province, but if that doesn’t help, check here; http://www.rentershotline.ca/searching.php
(I prepared Gatineau searches but for some reason the link reverts to all rent opportunities in Ontario, but I’m sure you can manage your own search.)
Will save some driving time, but you might have to pay some long distance fees for phone calls.
You’ll most likely have to pay or rent a moving truck, unless you have really nice friends with vans or pickups willing to help you move.
As for the culture in Québec, be warned, some are slightly xenophobic, but don’t let that discourage you, most of them will probably still invite you to go get drunk with them. :)