Provided that the lady was a genuine Romanov, she could have been Marina Petrovna (1892-1981), eldest daughter of GDk Peter Nicolaevitch.
She died in Six-Fours-les-Plages, a little village in Provence in the south of France.
I thought of asking about the identity of a Romanov relative. Perhaps somebody familiar with the family of Russia's last czar would know the answer ...
Years ago, one of my French teachers in high school was an American woman who herself didn't begin formally studying the language until the age of 16, but who had an international background (she was extremely well-traveled, since her husband was an army officer stationed in many places around the world). She recounted a trip she and her husband made to the Soviet Union, either in the late 1970's or the early 1980's: on her way, she stopped by Paris where she became acquainted with a "really nice old lady who was a relative (either a niece or great-niece) of the last czar of Russia."
The name Mrs. Nelson mentioned was Marina. However, I examined the family tree of Nicholas II and found out that he had only one niece through his surviving siblings, and her name was Irina. Plus, HH Princess Irina Alexandrovna of Russia died in 1970, when Mrs. Nelson was a young, unmarried woman. So she has to be ruled out as the old lady in question, with the likelihood that my teacher meant a great-niece.
But examining the next generation, the only Marina I ran across was the morganaut child of the czar's youngest nephew through his sister Xenia: Prince Vasily Alexandrovich married Princess Natalia Golitsyna and fathered Princess Marina Vasilievna, who was born in 1940 -- who could hardly have been the "old lady" described by my teacher. In fact, she would not have been many years older than Mrs. Nelson.
As such, she would not have been looking to make arrangements for her burial. For she asked the following as a favor from my teacher: "If you would be so kind, can you bring me back some Russian soil for my burial?" Sadly, Mrs. Nelson was unable to fulfill her request (she had carefully hidden the soil in her makeup kit, but the Soviet authorities confiscated it after examining her suitcase).
So my guess is that my teacher likely got her name wrong, and some other great-niece of the czar was the lady in question. But tracking down her identity is a lot like searching for a needle in a haystack, since the siblings of Nicholas II had/have numerous granddaughters, whatever might be said about daughters.
Can anybody guess who she might have been, on the basis of this description? Mrs. Nelson met her in Paris, and she likely would have been old enough to have ties to Russia -- likely born there (unlike the above-mentioned Marina, who was born in exile). Otherwise, it's difficult to see why she would have had such a sentimental attachment to the land and wanted some native soil for her eventual burial.
I did, in fact, ask my teacher in class "Est-ce que son père a tué Rasputin?", to which Mrs. Nelson replied (in French) something to the following effect: "That I wouldn't ask" or "That she wouldn't say". So no further clues there ...