You got it!!!
The French royal family of descendants of Louis XVI of the House of Bourbon is indeed, the Vanderbilt family. You missed one very symbolic event in their history, when Muriel Vanderbilt was married wearing the veil that Marie Antoinette wore at her wedding.
Nice work on the Utrecht Frankish connections. I had never quite figured out why they took the name of that little town Bildt. I do note that the French and Dutch flags are virtually identical, as is the Russian flag. Note that the veil came to Muriel from a Russian noble family.
What is the symbolism of the red white and blue that leads all these places to use it as their national colors?