Hindsight is 20/20 of course but I was always astonished that Napoleon III missed the threat from Prussia until it was too late. He should have seen the abortive attempt at doing the Erfurt Union as proof that Prussia was the one to watch. A FAR Alliance (France, Austria, Russia) supplemented by agreements with Denmark and some of the German states would have been better. The Crimean War was a mistake and so was backing Sardinia. Dumb, dumb, dumb.
I wouldn't say Napoléon III missed the Prussian threat. The first warning, as he took it, was the Prussian threat to intervene on Austria's side during the Italian War of 1859 which convinced Napoléon III to make peace with Austrians at Villafranca, at the cost of upsetting his Piedmontese allies who expected to go further as per the Plombières agreement.
Then, he hadn't any interest to ally with Denmark until after the Second Schleswig War as he needed to separate Prussia from Austria. The fact is that by the time of the 2nd Schleswig War, they were still allies, and France hadn't yet a major continental ally such as Russia (or the UK) to hold them in respect.
So that push back the possibility of an alliance between France and Denmark to the aftermath of the War of 1866.
There was a loose "alliance" IIRC from my reading of a book on the Fall of the Second Empire, that the Danish and Austrians were both in reserve when the Prussians went to war with the French. But it hinged on the French being able to score a victory over the Prussians, that the Austrians and the Danes (navy apparently) would jump into the fray. Of course, such a thing didn't happen and we all know the rest of the story.
How would a Danish and Austrian navy make any difference? It was a land war, the French navy alone greatly outclassed the Prussian one, not that it amounted to much. Also, Austria was in no shape to intervene in that war, as were the Danes.
French navy had indeed been able to blockade Prussia on its own.
I guess that loose alliance may be on the French planned expedition to North Germany where an expeditionary corps was planned to land. The plan was aborted because of early French defeats.