Could I tow with my car?

Tow what? A 50 foot travel trailer or a small pop up camper?

Yes. 

The manufacturer claims that all 2 litre engine variants (so most 2015 M3s) are capable of towing up to 1200kg. 

But they also stipulate that towing is only recommended with a trailer which has brakes on one or both axles.

They give no figures for unbraked trailers for liability reasons, and these days it’s either recommended (or mandatory in many countries) that all new trailer installations must be braked.

As a general rule of thumb, the maximum allowable weight of an unbaked trailer is one-third that of the braked weight limit: so that would be no more than 400kg for the Mazda 3. Having owned one, I’d say that even that limit is ambitious: personally I’d limit the maximum loaded weight of an unbraked trailer at 300kg. 

Those maximum weight recommendations from the manufacturer do not take account of gradients. If you face any long ascents or shorter steep hills in your area, I suggest that you knock 25% off those weight limits immediately. Same deal if on level ground but at altitude.

YOUR OWNER'S MANUAL WILL TELL YOU.

If you don't have the owner's manual, it's a free download from the Mazda website.

You can also Google the answer. It's not rocket science. I just checked and found the answer in eleven seconds, including typing the question. 

FAIL