Granted, a bit of a nonsensical scenario, but a prelude to a thought exercise. I used Denmark as the example because they are currently the only threat to Canadian sovereignty, over some island in the arctic archipelago.
If Canada were to conduct such an attack, how would the US respond?
Strictly speaking, the USA would be obliged to go to war with Canada, as Denmark is a member of NATO.
Of course, so is Canada. But the treaty states that an attack on one is considered an attack on all; it doesn’t exclude the case of one NATO country going berzerk. Since Canada would itself be in violation of the NATO treaty (article 2) you could reasonably say that by attacking Denmark, Canada would be giving up claim to being a member in good standing of the NATO alliance.
Of course, the US response would almost certainly not have to be full scale invasion; the United States Navy could cut the two nations off from one another with relative ease.
Of course, this damn near happened. Not between Canada and Denmark, but between Canada and Spain. The US expressed no opinion on the dispute (it was over fish) aside from wanting a peaceful settlement. Had the two countries actually started shooting at each other I’ve little doubt the USA would have exerted diplomatic pressure first. In the specific case of Canada, that USA can cripple the country through peaceful means, anyway.
Freaky. Has the US ever reacted much when a couple of First World nations go at it hammer and tongs?
Cool. There’s my answer. Thanks, RickJay. 
To play out the scenario - assuming a Danish ship was making a show of sovereignty over Canadian territory in the arctic, and was attacked for whatever reason by Canadian forces. Now, Denmark is involved, and I don’t know how big the Danish navy is, but presumably Canadian naval and coast guard forces could establish a presence in the region faster than Denmark could. I don’t see a full-scale invasion with the intent of occupation as likely, but presumably the coast of Greenland would have to be secured by deploying troops there. With all this going on, you’re saying that the United States navy would deploy to the arctic just to keep the peace, without taking sides?
Johnathan Miller (Dudley Moore and Peter Cook’s Beyond the Fringe partner) later pointed out from his doctor’s pespective on the plight of Secretary of State Alexander Haig as “shuttle diplomat” during Haig’s attempt to avert the Falklands War. Jumping on and off jets between Buenos Aires and London around the clock, he may have suffered the worst case of jet lag known to history, and despite his being West Point-trained and combat-tested, probably didn’t experience either a decent night’s sleep or pass a satisfactory stool for weeks aftewards.
This would sort of like watching your obnoxious mother in law taking on your idiot boss. Who do you root for?
(Disclaimer: My mother in law is a very nice person. My wife’s mother in law, on the other hand, is a royal pain in the neck.)
Forger Denmark. It’s the Belgians have had it coming for a long time now.
Like, say, France and Germany?
So it would matter which nation initiated the attack. If both sides deny that they started it… I just had a vision of some Admiral on the foredeck of a US destroyer, with a stern look in his eye and loudhailer in hand, shouting “All right you two - knock it off. Nobody gets the right of navigation back until I find out who fired the first shot!”
Seriously though - a territorial dispute which escalates to violence could be started by a single zealous soldier with a sidearm, in which case it is quite possible that NATO wouldn’t be able to figure out who started shooting first.
Considering their neighbor, I think both Belgium and Denmark have had enough abuse recently.
RickJay: When was the Spanish/Canadian confrontation you mentioned?
I just checked the CIA World Factbook.
Both countries have petroleum!
YEE-HA! IT’S PARTY TIME!
Invade 2 for the price of 1!
Of course…ahem…all in the intests of World Peace, naturally. 
It’s quite the leap to justify having to “secure” north Alberta as a result of a naval conflict in the arctic.
Pardon the hijack (and feel free to ignore it you like) but the OP made me wonder about a different scenario: Canada attacking Mexico. What would the reaction be to that?
Now that’s just silly.
Probably extremely unfavorable towards whoever violated US airspace first. Wouldn’t permission need to be obtained beforehand, else it is considered an invasion of the US? Otherwise, it’d be a pretty roundabout invasion.
I have this vision in my head of a long convoy of olive drab trucks backed up on the Ambassador Bridge between Detroit and Windsor:
What’s the purpose of your visit?
Just passing through on our way to Guadalajara.
How long will you be in the US?
3 days or so.
Are you bringing anything into the country?
You mean, besides the field artillery?
The U.S. would respond by continuing to not give a damn about the NHL lockout.
sniff I’m so proud! wipes away a tear
If we’re lucky, next it’ll be the NBA.
Returning to the OP, wouldn’t there have to be a new land bridge first so that the Mounties could gallop into Europe?
Befuddlement, and concern about how maybe terrorists have planted powerful drugs in the water coolers in Ottawa.