This is the debate going on in Wikipedia. June 13, 2021.
"Among her extramarital affairs, she is said to have had a relationship with the Count of Melfort whom she met at the Château de Saint-Cloud after the birth of her son. During the Revolution of 1789, Philippe-Égalité publicly claimed that his real father was not his mother's husband at all but instead a coachman at the Palais-Royal. This assertion was likely for political reasons to distance the ambitious Duke from the ancien regime. However recent DNA testing, to establish the Y-chromosome haplogroup and STR pattern of the House of Bourbon, has indeed confirmed the biological legitimacy of Louise Henriette's eldest son, Philippe-Égalité. As part of this project samples were taken from 3 living genealogical descendants of Louis XIII, namely Axel, Prince of Bourbon-Parma; Henri, Prince of Bourbon-Parma, and João Henrique, Prince of Orléans-Braganza. The former 2 are documented male line descendants of Philip V of Spain, who was a grandson of Louis XIV. The latter is a direct male line descendant of Philip I, Duke of Orleans - a younger brother of Louis XIV and the ancestor of Louise Henriette's husband. This study established that no non-paternity event happened along the three studied in-depth paternal lineages of these living donors, thus discounting rumors that the branch of Bourbon-Orleans could be illegitimate.
Actually, no, the assertion in the preceding paragraph is completely backwards and in error. Citing their exact same source, the study was entitled "Genetic genealogy reveals true Y haplogroup of House of Bourbon contradicting recent identification of the presumed remains of two French Kings" as published in the European Journal of Human Genetics in May 2014. One of their conclusions was that the DNA samples were very likely contaminated and that the genetic test therefore was probably inconclusive. However, the genetic researchers noted that "[f]inally, if the samples were indeed of both kings of France this would mean that there were at least two non-paternity events within the royal lineage of the House of Bourbon, namely that Henri IV was not the biological father of Louis XIII, next to another non-paternity between Louis, le Grand Dauphin and King Louis XVI. Non-paternity events—whether a man is not the biological father of his legal children—mainly occurs when the mother had sexual intercourse with a man other than the legal father or when an unreported adoption occurred."  This demonstrates that Louis Philippe Joseph d'Orleans probably was honest in disclosing that his biological father was probably the coachman at the "Palais-Royale." King Louis Philippe Joseph Egalite may very well have been "illegitimate."
We assert that there is a Carolingian-Stuart-Jacobite-Orleanist King living today!
There are some contemporary historians who have attempted to refute our finding that King Louis Philippe Joseph Egalite may have been illegitimate. These errant historians use the above scientific article published in the European Journal of Human Genetics to assert that there are no non-paternal events in the genetic lineage of the Orleans kings. First of all, the study attempted to use contaminated DNA samples of Louis XVI and Henri IV, both of whom would not help show dissimilar genetic information in King Louis Philippe Joseph Egalite. Second, these errant historians misread or misunderstood the scientific article's conclusion. They got it wrong. Our hypothesis that King Egalite may have been the son of Bonnie Charles Stuart remains to be proper challenged, refuted, and debunked. Read on.
Larmuseau, M. H; Delorme, P; Germain, P; Vanderheyden, N; Gilissen, A; Van Geystelen, A; Cassiman, J. J; Decorte, R (2013). "Genetic genealogy reveals true y haplogroup of House of Bourbon contradicting recent identification of the presumed remains of two French Kings". European Journal of Human Genetics. 22 (5): 681–687. doi:10.1038/ejhg.2013.211. PMC 3992573. PMID 24105374.
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Louise Henriette of Bourbon,
wife of Louis Philippe I, the Fat.
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