Reverso shows no translation, merely the use of the American term.
It appears to be the case that for the time being there is no French term and that people in need to mention this concept simply use "bleisure". I deduce that from additional confirmations from some articles though.
There is apparently an ambiguity at the outset in the definition of this term, an apparent unease in the definition; several dictionaries do not agree with one another.
(Word Sense) bleisure (uncountable)
(colloquial) Travel or another activity that combines business and leisure.
(Macmillan) bleisure
business + leisure = bleisure; it is a portmanteau
A new breed of traveler is mixing business with leisure on so-called “bleisure” trips.
(Collins)
Bleisure
New Word Suggestion
The blurry line between business and leisure trips; the office sends you to Scotland, for example, and you invite your spouse along to get the most out of your corporate-paid hotel room, etc.
Submitted By: DavedWachsman3 - 27/09/2012
Approval Status: Reject – not enough evidence
(Urban) Business and leisure combined, commonly used in the hospitality industry.
A: Are you travelling for business or leisure mate?
B: I'm travelling for bleisure actually.
There is in this first article below one of the interpretations: "bleisure" as "bleisure trip".
Voyages d’affaires : quand le travail peut rimer avec plaisir Une étude de la société de réservation de voyages Booking.com révèle que près de la moitié des voyageurs d’affaires ont prolongé leur voyage d’affaires pour le plaisir et qu’un troisième prévoit de le faire à nouveau. Le concept de voyage qui combine travail et plaisir est appelé « bleisure » et constitue une tendance croissante dans le secteur des voyages d’affaires.
In the second article I could find that the term is still being dealt with as a foreign term since it is not only used between quotes, but complemented with a capital. The same association of the term with only travel is found again in this article (four occurrences).
Hervé Kozar, Transavia : « Travail ou plaisir, pourquoi choisir ? » Transavia ne cache plus ses ambitions dans le voyage d’affaires et se positionne en particulier sur le "Bleisure", une tendance de plus en plus naturelle, notamment pour la génération Y, à associer déplacements professionnels et plaisir de voyager. La compagnie filiale d’Air France lance le 5 septembre une campagne de communication de conquête, appuyée par un sondage CSA édifiant.
In this last article 13 occurrences are found of this American term, which shows that there is a serious intention of using it as a translation. No quotes are used but usage is not consistent (upper-case for the first letter, no upper-case, no article, article); the article is dedicated to the concept of bleisure.
(7 conseils pour que les hôtels attirent plus de vacanciers)
However, the shy emergence of two terms made up from french words can be found in this article (and they are inexact translations), plus the mention of a would-be synonym, "bizcation", which apparently is considered just as good a candidate for the translation of "bleisure".
- voyage de plaisir (It is really something else (no business, only pleasure))
- voyage de plaisance (same remark as above)
- bizcation (entreprise vacances)
From what can be read, it is for now safer to translate "bleisure" as "bleisure".
There are possibilities that do not seem very good, but which finally might become appealing.
- bleisure traveler → voyageur de plaisir, voyageur de plaisance (It is really something else (no business, only pleasure))
- bleisure trip → voyage d'agrément (same remark as above)