Based on the evidence we do have, it seems highly unlikely.

1.) It was not until the French Revolution that France adopted the guillotine as its primary method of execution. This was a direct result of Enlightenment thought, as death by guillotine was thought to be quicker, harder to botch and altogether more humane than previous methods of execution. The first person executed by guillotine, a certain Nicolas Pelletier, was sentenced in 1791 and died in 1792.

France transferred administration of La Louisiane to Spain via the Treaty of Fontainebleau (which took place in several stages) throughout the late 1760s, when the guillotine's use was not yet established as a governmental norm.

2.) In 1760s Louisiana, the aforementioned transfer proved quite unpopular among the native Creoles, who revolted against Spanish rule. It may be noteworthy that the Creole ringleaders were shot—not guillotined—as a result. This was quite a high-profile matter of the kind which may well have merited a public guillotining in Revolutionary France, so we can likely assume the Louisianais were not guillotining people at that time. (That said, this execution was performed by a Spanish administration rather than a French one.)

3.) Regarding the later period, when France briefly retook Louisiana before selling it to the US, I can do no better than to cite the American Quarterly Catholic Review, Volume 12, published in 1887, which recounts an episode in which an Ursuline nun roundly criticized the French Republic before the French colonial prefect, Pierre Clément de Laussat. Despite the Ursulines' apparent fear of persecution, the passage concludes that "no guillotine was set up in Louisiana, and Laussat gallantly excused the lady on account of her great age."

So the evidence suggests that no, the guillotine was never introduced to Louisiana.

(It is harder to cite a lack of evidence than an abundance of evidence, so please forgive the relative lack of sourcing here.)