Depending, theoretically, on what sort of property is concerned. 'Beneficiary' might be a safe bet: "The definition of a beneficiary is quite broad, which means it includes both legatees and devisees."
(anything in double quotes here can be found on the Ouèbbhe)

"What is the difference between a legatee and a devisee? Applying the archaic legal definitions, the difference between a legatee and a devisee is the kind of property they inherit. A legatee inherits personal property (jewelry, vehicles, cash, etc.) while a devisee inherits real property, such as the family home."

"Technically, a devisee inherits real property, while a legatee inherits personal property. Despite this technicality, “legatee” is often used in North Carolina to describe a person who takes any sort of property pursuant to a will."

"Although the term legatee is generally used to refer to individuals who inherit from a will regardless of whether it was real property or personal property, an individual who inherits real property from a will is known as a devisee."

"Legatees, devisees, beneficiaries: Those to whom property is given by will or codicil or on an intestacy are beneficiaries. Strictly, a gift of personalty (anything except a freehold) is a bequest to a legatee, and a gift of a freehold is a devise to a devisee, but the two forms of wording are interchangeable if there is sufficient context in the will."

I haven't made a far-reaching search for the à titre privé bit, but at first sight it appears to revolve around taxes on inheritance by diplomatic personnel:

"L’agent diplomatique jouit de l’immunité de la juridiction pénale de l’État accréditaire. Il jouit également de l’immunité de sa juridiction civile et administrative, sauf s’il s’agit :
[...]
b. D’une action concernant une succession, dans laquelle l’agent diplomatique figure comme exécuteur testamentaire, administrateur, héritier ou légataire, à titre privé et non pas au nom de l’État accréditant"
"1.A diplomatic agent shall enjoy immunity from the criminal jurisdiction of the receiving State. He shall also enjoy immunity from its civil and administrative jurisdiction, except in the case of:
[...]
unless he holds it on behalf of the sending State for the purposes of the mission;
(b) An action relating to succession in which the diplomatic agent is involved as executor, administrator, heir or legatee as a private person and not on behalf of the sending State;"
[Vienna Convention on Diplomatic Relations, Article 31]