Credit card transactions are a good start. If you were at work in your home country, what about a statement from your co-workers?

No implication of using e-gates, even if you talk to a border official they don't stamp a EU passport.

I must say, as an ex-Montrealer I'm curious as well!

what is the standard of proof for the alleged offence
 

I am not (as) convinced that this is as simple as proving you were out of the country........
Under Quebec law, there is a concept known as absolute liability. If, for example, my car is parked illegally, its not a defense to say I was outside the country. The car is registered in my name and I am absolutely liable for any infractions.
The OP avoided saying what the offence is? Until we know more details, I (for one) am not of the view that demonstrating one is out of the country is a get out of jail free card.
Moving offences are even worse IMO. In Ontario, the officer is a no show, I walk. Not in la belle province. Proof in PQ is admissable by means of an affadavit.
The bottom line? I need to know more about the offence first before providing an opinion.

Even if you send in all the proof if the world they will take your case to city court, then before the procedure they will make you an offer or withdraw. Even in the most clear cut situations La Ville De Montreal never backs down. Be prepared to have this drag on

Incidentally how did this end?

The court hasn't even managed to assign a prosecutor yet that I could talk to / send docs to, despite the hearing in court being scheduled for early Dec. The speed at which they move is really mind-boggling.... :rolleyes: