Where to find missing information about an ancestor?

Hello, I am very new to genealogy and I have a difficult task at hand.

My grand mother asked me to see if I could find anything about her cousin who left France after WW2 to marry an American soldier. My gm is in her 90s and doesn't remember most of the precious details that could be useful when looking for her cousin.

I only know her first name and maiden name as well as the fact that she married an American. My gm cannot remember the year she was born or what American state she lived in after her wedding.

How could I found this woman's married name?

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