So I called BA and they confirmed the answer of Andriyko, the class fare of the LHR-TLS is indeed the wrong one to be able to have the cheapest PE on YUL-LHR. I told them about the AA price but they can't match it.

So I looked at the LHR-Paris on ExpertFlyer and sure enough there are several flights with K and the price on BA is even a little bit cheaper than on AA. So I booked YUL-LHR-ORY and UuA for 20k avios.

Thank you all for the help (specially Andriyko!). I learnt a lot

Matthieu