why does France (or the USA and 180 other states) have diplomatic relations and send ambassadors to Vatican City but not to Mecca, Jerusalem, or any other "religious" city?
From C.P.G.Grey Vatican City Explained: "The King of Vatican City (the Pope) has absolute unchecked power within the country's borders and his presence makes Vatican City one of only six remaining absolute monarchies in the world. The King's absolute power is one reason why Vatican City cannot join the European Union because only democracies are allowed." C.P.G. Grey, Vatican City Explained.
The Holy See was made a nonmember permanent observer of the United Nations in 1964 and given full rights of membership except voting in 2004. The only other "nonmember" is the State of Palestine. Israel is not considered "a Jewish state."
The Center for Reproductive Law and Policy: "..the status of the Holy See as a nonmember permanent observer to the UN is questionable. Moreover, there are doubts about whether in 1964 the UN is creating a precedent for similar claims by other religions. To ensure that the UN does not promote one particular religious view religious entities such as the Roman Catholic Church should not be permitted to participate in that body as nonmember states."
We can only hope France will tell the Vatican it is not interested in sending an ambassador and 180 other states will follow.