Alex,
The files regarding Canada-UK troopships can be found in the Library and Archives Canada "Directorate of Movements" files.
Using your presumed Embarkation date of 13 or 14 Sept 1943, I used this search
https://www.bac-lac.gc.ca/eng/collec...perator_2=AND&
to determine that the likely candidate is the Queen Elizabeth:
https://www.bac-lac.gc.ca/eng/Collec...61785072371167
Unfortunately the microfilm that contains this file (C-5691) is not available on-line. If you know someone in Ottawa with access to LAC, they can use the information in the above link to organize viewing the appropriate microfilm.
I did manage to find the file for the Westbound voyage of the Queen Elizabeth which arrived in Halifax on 3 Sep 1943. Please have a look through this file for the type of information that you can likely expect. (I did notice a document related to a group of gunners who were to guard the ship during it's stay in Halifax, and then depart with the ship):
https://heritage.canadiana.ca/view/o...9/4985?r=0&s=2
I am not familiar any resources that can help with your search for the UK-France voyage.
Regards,
Colin