Note that as of September 2021, no lenders are currently offering mortgages to American buyers over 55 years.
French Mortgage Eligibility: How Much Can You Borrow? – FrenchEntrée (frenchentree.com)
Americans can still buy a property but need to be cash buyers.
As noted often on this blog, it is wise to travel when young – and if you wish to get experience living overseas, consider study abroad or work abroad options available earlier in your career. Many professional careers provide such options – including doing study abroad or graduate study abroad, or working in other countries.
I was surprised to find these limitations on buying properties in France. In fact, the above linked article says anyone at age 75 or over cannot carry a mortgage. If a French citizen at age 65 were to take out a mortgage, it must be completely paid off with in ten years, before age 75.