A tailor could certainly alter the fit down from XXL to M. All that's need is to have your torso length, arm length and chest size measured. Where I live, there are cheap tailor shops that can do this. Don't know about your location.
I'm not a professional tailor or anything but I think it would depend on the jacket-- I didn't see a pic (maybe it just didn't show for me?) even though your post said "this jacket".
In any case, if the jacket has a pattern of some sort that could affect a tailor's ability to take a XXL jacket down to M. Further, by taking a jacket from XXL to M, you are basically asking the tailor to "make" a jacket for you out of the fabric of the XXL jacket more than actually simply altering it so the cost will likely be pretty high if you wanted even reasonable quality work.