The poop will be little, maybe 1-2cm long and 3-4mm in diameter. Healthy frog poop will crust up after a day and can easily be cleaned up. If you break it apart you may be able to get an idea of what it's eating, some parts of insects can pass through undigested (wings, beetle shells, etc.). It's probably in a sort of 'winter slow-down', so it's not likely to poo every day.

If you are leaving it free range, you should provide a shallow source of fresh water for it to soak in. A plastic shoebox with no lid with 1/2 inch of water and a branch or two from outside so it can easily climb out might be a good idea. Frogs do 'pee', but in my experience greys like to do it while soaking so this would help contain it. The volume of 'pee' is small, largely inoffensive, and pretty dilute if the frog is well hydrated.

If you have sow bugs or roly polys in your basement you could collect them in a plastic shoebox with no lid and put them near the frog, watching them eat is fun and educational.

You might try contacting Untitled 1 or Reptiles Rock! Ottawa, Ontario Reptile Education, Birthday Parties, Summer Camp or other herpetological minded folk in Ottawa to find someone to take it off your hands. My concern with free range basement living is it ending up lost in a drain or finding the pilot light for a furnace, or other danger down there.