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Jebus was aquired by King David who was at the time King of Israel.
(Isn’t that how the story goes?)

Story perhaps. Jebus followers argue about which version of the Good Book is the real Good Book.

As for modern Israel, its status pursuant to UN resolutions called for Jerusalem to have international status. This is reflected by the fact that fewer than a half dozen nations have their embassy in Jerusalem, but rather in Tel Aviv.

France had a claim on Jerusalem.

https://en.wikipedia.org/wiki/Status_of_Jerusalem#French_claims_in_Jerusalem

There are four sites in Jerusalem claimed by France as "Domaine national français", which are based on claimed French acquisitions predating the formation of the State of Israel, and based on the former French Protectorate of Jerusalem (also known as capitulations), which was abolished in 1923. These sites are:
Church of the Pater Noster, also known as the Sanctuary of the Eleona
Benedictine monastery in Abu Ghosh
Tombs of the Kings
Church of Saint Anne.
French presidents have claimed that the Church of Saint Anne in Jerusalem, for example, comes under French protection, is owned by its government, and is French territory. The Israeli government has not made any public statement relating to the French claims.

And the Holy See has a claim.

https://www.jewishvirtuallibrary.org/jerusalem-and-the-holy-see

Interview with His Excellency Archbishop Jean-Louis Tauran, foreign minister of the Vatican State (1999).

TAURAN: In the beginning, the Holy See supported the proposal for internationalizing the territory, the "corpus separatum" called for by United Nations General Assembly Resolution 181 of November 29, 1947.
In the years that followed, although the objective of internationalization was shown to be unattainable, the Holy See continued to call for the protection of the Holy City's identity. It consistently drew attention to the need for an international commitment in this regard. To this end, the Holy See has consistently called for an international juridical instrument, which is what is meant by the phrase "an internationally guaranteed special status."
At the present time, while maintaining the request for a special status internationally guaranteed, emphasis moves to Jerusalem in a global context and to the preservation of its identity and vocation: the holy places, the areas surrounding them, guarantees for everybody of their own cultural and religious identity, freedom of religion and conscience for the inhabitants and the pilgrims, and the broader cultural dimension.