I receive an invitation from a China School to teach French, from June 1, 2012 to November 30, 2012.

If you have invitation letter from China, you can start your application now, so, just reserve your air ticket first. Generally, China visa is valid for 3 months from issue date. You'd better enter at the end of May before the teaching begin. The regular processing takes 4 working days. If you live in the area under Consular Jurisdiction of Vancouver or Toronto, your application should be submitted to Chinese Visa Application Service Center (CVASC).