The short answer would be, armories.

The 17th c. saw a lot of advances in muskets. The French introduced the flintlock in the early 1600's, and it grew in popularity during the Thirty Years War. At the end of the century there was also the introduction of the bayonet, something that could be mounted on the muzzle , but would still allow the musket to be fired. There was also an increase in the size of armies- Louis XIV especially loved war. There was also a recognition that it was better for soldiers to be carrying the same gun- that, at least, used the same ammunition. So, there were good reasons to build a lot of muskets of a new type at the end of the century.

I am not sure about all the other countries, but in England, at least, the previous practice had been for a colonel to raise a regiment and then to be given money to buy their muskets, uniforms. This power was sometimes abused- the colonel could take the money for good equipment, buy junk, and pocket the difference. But at the end of the 17th c. the practice changed, and with the introduction of the New Land Pattern, AKA the Brown Bess, there were several reforms. Things like locks, barrels and buttplates were made in quantity , most all in Birmingham- for metalwork, that had the advantage of nearby iron and coal. The pre-industrial way to efficiently produce something was to specialize, so a big shop that made gun barrels would have smiths and hammermen who did nothing but that, as well as special forging dies, and very likely water-powered tilt hammers for doing the welds and water-powered boring machines for reaming out the bores. The Gun Quarter of Birmingham would have a lot of highly-specialized shops, so a worker in one might do nothing all day but file lock parts, or grind bayonets.

All the metal pieces would be shipped to the Tower of London. It was there that the barrels would be proofed, tested to make sure they were good, and locks assessed for quality. It was there that the actual pattern for the musket was kept, and London gunsmith shops would contract to stock the muskets, i.e. make gunstocks according to the pattern, getting all the metal bits from the Tower.

Eventually it was decided that the system was not working as well as it should- the Napoleonic Wars required a very big increase in the military, and the result was something of a mess...That led to the creation of the Royal Small Arms Factory at Enfield in 1816. That was able to incorporate industrial production methods later in the century.

France would also create armories, taking advantage of specialization as well. Louis XIV having lots of places he wanted to invade, France built them somewhat earlier than England- the armory in St. Etienne in 1669, the one in Tulle in 1690. For the French armories there is a very useful source, the 1751 Encyclopedia of Denis Diderot, that illustrates a lot of the techniques. A French armorer, Honoré LeBlanc, would be the first in the late 18th c. to suggest standardizing all the parts of a musket, so that they would interchange. In the pre-indistrial craft world of the time this was hard to do; LeBlanc had to require his workers to not just fit parts together, but make them to a very precise pattern. Though it did not catch on in France, this deeply impressed the American ambassador, Thomas Jefferson, and he brought the idea back to the US with him, where it would be adopted by the John Hall shop at the Harper's Ferry Armory in 1819, and the Springfield Armory as well. With the advent of industrial machine tools, repeatable processes became possible and interchangeable parts as well. This then became known as Armory Practice, or sometimes the American System, and became an important part of industrial manufacturing generally.

Alder, K. (1997). Innovation and Amnesia: Engineering Rationality and the Fate of Interchangeable Parts Manufacturing in France. Technology and Culture, 38(2), 273–311. https://doi.org/10.2307/3107124