The so-called "Ring of Fire" crows' nest with its 31 cannons was built as a fully-working version out of a mass of wood in only 14 days by a German company called 'pyro.labs berlin'. It is on display in the Babelsberg movie studio film park.
The substitute for The Royal Palace of Louvre in the movie (Versailles was built almost half a century later than the time this story takes place) is a German palace, the Fürstbischöfliche Residenz (the prince-bishop's palace) in Würzburg, Lower Franconia, Bavaria.
At the start of the film The Three Musketeers & D'Artagnan show how they are representative of the four elements: Athos represents water, Porthos represents earth, Aramis represents wind, and D'Artagnan represents fire.
The dance music near the end is appropriate for the time period. It's a gavotte from Terpsichore, a large collection of dance music published in 1612 by German composer and musician Michael Praetorius. The original novel begins in 1625, so the Terpsichore collection would have been known then.
In the scene following the Musketeers' fight with the Cardinal's men, d'Artagnan and the Musketeers walk through the portal of the "rathaus" (town hall) in Bamberg, Bavaria in Germany. The rathaus sits astride the river Regnitz which runs through the city. To the left in the background, a half timber house that seems to float over the river can be seen. This is the Hotel Restaurant St. Nepomuk.