Probably not. It seems to have existed as a traditional right, but was almost never exercised.
Wikipedia denies the existence of this right, citing Albrecht Classen's The Medieval Chastity Belt.
Snopes concurs, citing Encyclopedia Britannica, 15th ed., 10.610:
[The droit du seigneur] is paralleled in various primitive societies, but the evidence of its existence in Europe is almost all indirect, involving records of the redemption dues paid by the vassal to avoid enforcement, not of actual enforcement. Many intellectual investigations have been devoted to the problem, but, although it seems possible that such a custom may have existed for a short time at a very early date in parts of France and Italy, it certainly never existed elsewhere.
(That page conflicts with itself... Earlier, it notes that "First night customs survived in parts of Europe into the Middle Ages (as the droit du seigneur)", but this isn't backed up by a source.)
Both the above pages also cite The Lord's First Night: The Myth of the Droit de Cuissage.
A review paper (Wettlaufer, Jörg. "The jus primae noctis as a male power display: A review of historic sources with evolutionary interpretation" in Evolution and Human Behavior Vol. 21: No. 2) opens with
The existence of a jus primae noctis in the Middle Ages was an eagerly disputed topic in the nineteenth century (Hanauer, 1893; Pfannenschmid, 1883; Schmidt, 1881, 1884; cf.
Schmidt-Bleibtreu, 1988). Although most historians would agree today that there is no authentic proof of the actual exercise of the custom in the Middle Ages, disagreements persist
concerning the origin, meaning, and development of a widespread popular belief in this alleged “right” and the existence of symbolic gestures associated with it (Barros, 1993;
Boureau, 1995; Sorlin, 1987; Wettlaufer, 1994, 1999).
On the other hand, the same paper also notes that the droit du seigneur was codified in law in at least one place:
... a Swiss village in the vicinity of Zurich. In a customal from about 1400 A.D., the rights of the inhabitants of Maur
were itemized ... “Item, who wants to enter the holy state of marriage in the village
and court of Maur, whoever he may be, shall hand over the woman to Us for the first night or
he may buy her out, as it is custom and tradition and written in the old customals. If he
doesn’t do so, he must pay a fine of 30 pennies” (STAZ [Staatsarchiv des Kantons Zürich]. Urkunden Stadt und Land Nr. 2563; copy of the 15th century, cf. Wettlaufer, 1999: 251).
However, despite this codification, no record of actual exercise of this "right" survives, from anywhere in medieval Europe:
In a text of mediation between the two parties (the peasants and lords of Catalonia), the peasants accused the lords of practicing symbolic acts on the
wedding night to demonstrate their power and lordship. ... Furthermore, the lords were accused of having
abused these symbolic acts for purpose of sexual harassment. The lords, on the other hand,
denied all this ... This is the only medieval testimony indicating anything like actual sexual relations between the lords and the peasant brides in the context of the right of the first night, and the evidence concerns only sexual harassment, not sexual intercourse.