The comma before the word normally is not needed. Process must be plural as well because of the teaching process and learning process. Each is a noun in the accusative position. I also would restructure that sentence this way, "There is an English Department where all English teachers meet for an hour per week to organise jointly the teaching and the learning processes of the subject."

It is of interest that the word " organize " is not spelled as " organise " except outside of North America and Canada. Some therefore would say you misspelled the word organize 'I have a similar problem with the Spanish use of " hubiera " and " hubiese " . My computer marks " hubiese " as a mistake