if you are paid by Minstere du Travail to finish secondary 4 and 5th full time and paid daycare expenses, can higher earner claim the daycare as other spouse was full time student?

Yes, the higher income earner can claim.  Here is the definition of an Educational Program for the purposes of determining if the lower-income earner qualifies as a student:

Educational program
An educational program has to be offered by a secondary school,
college, university, or other designated educational institution.
This includes any institution certified by the Minister of Employment
and Social Development Canada for courses that develop or
improve occupational skills. An eligible program has to last at least
three consecutive weeks.
Full-time educational program requires students to spend at least
10 hours a week on courses or work in the program.
Part-time educational program requires students to spend at least
12 hours in a calendar month on courses in the program.