The Government of Quebec works with the Federal Government of Canada to run and manage the Quebec Skilled Worker Program (QSWP). This program helps highly trained and qualified overseas nationals to come and work in Quebec as skilled workers.
Applicants applying for the QSWP are evaluated on a grid of factors for selection. And the ones who score adequate points receive the CSQ - Quebec Selection Certificate. Applicants can use this certificate to apply for a PR Visa for Canada.
The Immigration Department of Quebec works independently of the IRCC. Also, Quebec is not a part of the Express Entry Program. Hence it does not choose qualified applicants through the Express Entry pool.
Applicants need to apply directly to the Governing Body of Quebec. You must submit an Expression of Interest (EOI ) to the Quebec Ministry of Immigration - Ministre de immigration if you want to settle in Quebec (permanently). After this step, you may receive an invitation to put forward an application for permanent selection if your skills and qualifications successfully meet the criteria set by the province. You get brownie points if you have a better command of French than English.