"I will have to provide a valid address (which I do not have however)."


Actually you won't. They do some validation of address for US but not elsewhere. Just put your normal address but put CAnada as the country.

"Will they not try to send some mail to this address (cards, welcome package or things like that). Can it be a problem ?"

You might miss out on a flimsy card if you are unlikely. Or join in advance so that you have all the joining info to your france address and just change it to Canada before you set off. Just get it changed back when you have done your CX/BA flights and your platinum card will arrive at the correct address

Changing countries for this is a doddle on AAs scheme

Dave