Author of The Mystery of Capitalism and the NYTimes article cited above, Hernando de Soto is a well-known Peruvian economist who has perhaps been a little careless with his words. Some (or even many) of the 'technocrats' de Soto refers to may have been hired by Colbert, but Colbert died (1683) before the industrial code restricting cotton importing / printing was enacted (1686). Further, not all the deaths were by execution and many may have had more to do with religious persecution.
The background to this is the importation of cheap Indian cotton (Calico) and the printing of colourful patterns on this material. The end product was much cheaper than other materials and thus increasingly led to calls for protectionist measures in several European countries from those with economic interests in other materials.
16,000 people may have died, but when exactly is unclear. The 'when' is important to the OP's question because Jean-Baptiste Colbert died in 1683, whereas the (draconian) law against cotton importers and printers (aimed at protecting the market for the more expensive silk, wool, linen and hemp products) was only enacted in 1686. Further, the deaths appear to have mostly occurred during and after this date. The use of 'Colbert's technocrats' is thus a little careless in its lack of precision. Also, not all of the deaths were through executions.
The immediate source of this number would appear to be Mercantilism by the Swedish economic historian Eli Heckscher (of Heckscher–Ohlin model fame), published in 1955 (3 years after the author's death).
It is estimated that the economic measures taken in this connection
cost the lives of some 16 000 people, partly through executions and
partly through armed affrays, without reckoning the unknown but
certainly much larger number of people who were sent to the galleys or
punished in other ways.
Unfortunately, it's not clear where this number originally comes from. Another potential problem with this number is that that the ban enacted in 1686 came only a year after the Edict of Fontainebleau (Oct 1685). According to L'histoire du coton entre 1689 et 1746, this
signe la fin de la paix
entre catholiques et protestants. Environ 30 000 artisans huguenots
(principalement des tisserands, teinturiers, imprimeurs sur tissus et
des des négociant et ouvriers en soie) s’exilent alors en masse en
Suisse et à Spitalfield, un quartier londonien créé à ce moment
Translation: marks the end of peace between Catholics and Protestants. About 30,000 Huguenot craftsmen (mainly weavers, dyers, cloth printers and traders and silk workers) then mass-exile themselves to Switzerland and Spitalfields, a London neighborhood created at that time
As many of the printers of patterns on Calico were Huguenots, this raises the question as to whether all the deaths can solely be attributed to the 1686 ban on this activity.
This article, excerpted from An Austrian Perspective on the History of Economic Thought, vol. 1, provides other details relating to the controversy over cotton imports / printing:
In 1700, the French government went all the way: an absolute ban on
every aspect of calicoes including their use in consumption.
Government spies had a hysterical field day: "peering into coaches and
private houses and reporting that the governess of the Marquis de
Cormoy had been seen at her window clothed in calico of a white
background with big red flowers, almost new, or that the wife of a
lemonade-seller had been seen in her shop in a casquin of calico."
Ultimately, the 1686 ban proved not only costly in lives but also to the economic well-being of France, at the same time as being of great benefit to Holland and England in particular, even though cotton weavers and printers were also subjected to protectionist laws and mistreatment in the latter country.