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The French word that was translated to stud was ferret. I don't actually see any justification for translating ferret here as stud, as I will explain later.

To explain how the diamonds were worn first, these twelve diamond ferrets were part of a decoration meant to be worn on a shoulder. It was made of six blue ribbons woven or knotted together. The twelve ferrets were ornamental tips attached to the ends of the ribbons.

The rest of the answer contains the justification for this statement. To see what ferret means, let us look at the relevant definition from the Larousse dictionnaire de français. This is

Petit bout (en métal, en pierre précieuse, etc.) d'une aiguillette.
Small tip (of metal, gemstone, etc.) of an aiguillette.

So what is an aiguillette? The English translation is aiguillette, but this won't help modern readers because the word has largely fallen out of use in both English and French (because aiguillettes aren't used much anymore). Larousse says that an aiguillette is

Cordon, ganse ou tresse, ferré aux deux bouts, ayant, jusqu'au règne de Louis XIV, servi à fermer ou à garnir les vêtements.
Cord or braid, tipped with metal at both ends, that until the reign of Louis XIV served to fasten or decorate clothing.

So an aguillette was a short length of cord or braid, tipped at both ends, often with precious metal or gemstones, that was used to fasten clothing closed, or which was worn purely for decoration.

One can see pictures of them in English Wikipedia. This says

Portraits of the 16th and 17th centuries show that aiglets or metal tips could be functional or purely decorative, though many were used to "close" seams and slashes that are not always apparent on dark garments in portraits. They were made in matched sets, might be of silver, silver-gilt, or gold, and were worn in masses.

Here is a 1562 picture of Lord High Admiral Clinton wearing a doublet fastened by aiguillettes, from Wikipedia.

Lord High Admiral Clinton in an arming doublet of 1562

So were the diamonds on aiguillettes? If they were, stud might be a reasonable translation of ferret, because a stud is a piece of jewelry that you use to fasten two buttonholes together, and similarly an aiguillette is a piece of jewelry you use to fasten your clothing.

However, in this case, the ferrets were not on aiguillettes, although they were indeed on the ends of ribbons.

The first time we see the ferrets being worn is:

elle [la reine] avait un chapeau de feutre avec des plumes bleues, un surtout en velours gris perle rattaché avec des agrafes de diamants, et une jupe de satin bleu toute brodée d'argent. Sur son épaule gauche étincelaient les ferrets soutenus par un noeud de même couleur que les plumes et la jupe.

She [The Queen] wore a felt hat with blue feathers, an overdress of gray-pearl velvet, fastened with diamond clasps, and a skirt of blue satin, embroidered with silver. On her left shoulder sparkled the diamond ferrets, on a knot of the same color as the plumes and the skirt.

A later description of the diamonds in Les Trois Mousquetaires follows:

Tenez, lui dit-il en tirant du coffre un gros noeud de ruban bleu tout étincelant de diamants; tenez, voici ces précieux ferrets ...
“Here,” said he, drawing from the casket a large knot of blue ribbon all glittering with diamonds, “here are the precious ferrets ...

Note that the French word noeud is broader than the English word knot; a bow would also be called a noeud.

So the ferrets are in a large decoration made of blue ribbon. We also find that this was meant to be worn on a shoulder. This decoration must then be made of six blue ribbons knotted or woven together somehow, and the diamonds are on pieces of jewelry which are affixed to the twelve ends of these six ribbons.

Note: the English translations from The Three Musketeers above are my modifications of the translation on Project Gutenberg.