I've just spoken to a very nice lady at the La Sarre Tourist Information Office. (Phone 00-1-819-333-2214). She told me that the nearest airport served by commercial flights is Rouyn-Noranda, which is about 1 hour's drive from La Sarre.
Services to Rouyn-Noranda are listed on Wikipedia:
http://en.wikipedia.org/wiki/Rouyn-Noranda_Airport
The Manchester Airport website shows the only Canadian destinations served directly from there are Calgary, Toronto and Vancouver, which means that you can't to Roun-Noranda in just two stages.
One possible route would be with BA to Montréal Trudeau Airport (via Heathrow) and then with whichever one of the three airlines listed in Wikipedia's link can get you to Rouyn-Noranda most conveniently. Alternatively, since Air Canada operate from Heathrow to Montreal, they might be able to offer through ticketing on to Rouyn-Noranda (using their Air Canada Express service).
This website, operated by the broker Car Rental Republic, might help you hire a car:
http://rouyn-norandaairportcarrental.com/
If you need further assistance, please tell us when you need to travel.
Chris