Quebec law will apply.
these are the steps for Quebec
1.) Submit a sponsorship application to the Government of Canada
2.) Submit an undertaking application to the Government of Québec
If your sponsorship application is approved, CIC will notify you by letter or email inviting you to continue the process by submitting an undertaking application to the MICC and confirming the acceptance of your application.
This confirmation is very important since it constitutes proof that your sponsorship application was submitted to and approved by CIC.
* You must forward a copy of this confirmation (letter or email) to the MICC when submitting your undertaking application, accompanied by the fees payable and all required forms.
3.) Ask the person you are sponsoring to complete certain procedures, namely, applying for a
Québec Selection Certificate and permanent residence.
So, once you have moved to QC (depends after which step of the above), you have to inform CIC (that you have moved to QC) and ask them to send you the letter or the email inviting you to continue the process by submitting an undertaking application to the MICC (step 2 above). Only after getting this letter, you may continue with MICC (Quebec) and then proceed for the CSQ.
Read more at
http://www.immigration-quebec.gouv.qc.ca/en/immigrate-settle/sponsors-sponsored/apply/index.html
Hope this helps.