Is feasible to visit Old Montreal or Downtown during a 12-hour layover?

I will be flying Mexico City to Paris, with a layover in Montreal (YUL). I will arrive in Montreal at 7:40am on a Saturday, and my departure is at 7:50pm the same day, giving me 12 hours on the ground.

Realistically, is it feasible to leave the airport, visit downtown or Old Montreal with enough time to eat lunch, visit a museum or two, and return to the airport?

Specifically, for this to be considered "feasible":

• Does the YUL airport offer baggage lockers? If so, what is the cost?
• What is the transportation time and cost to/from YUL to Downtown or to Old Montreal? I prefer public transport, but would consider a taxi if the circumstances dictate.
• How long is it likely to take to get through customs/security upon arrival?
• How early should I arrive at the airport for my 7:50pm flight, to get through security, etc, before my departure? I will only be traveling with a carry-on, so no luggage to check.