A Jewish or not? What I do now?

While digging in the family history, I found my great grand mother on maternal line was Jewish. She was from a non practicing liberal family in the Lorraine region of France, and married an Italian immigrant. When the WWII broke out, they both went into hiding in the free zone of France, her for obvious reasons, him because he was still officially an Italian, and wanted to avoid being drafted in Mussolini’s army. They escaped the war with their 3 daughters (including my grandma), who were raised Christians, as well as my mother and I. My grandma’s death 2 months ago led me to the realisation that I didn’t know the story of this part of my family. So I asked, and here the result.

How do I connect with those roots? I know no Jewish person. I have been in Israel last year, before doing this research, and have been amazed at the achievement of the people there. I was rather pro-palestine before going, I got back pro-israël. My faith is christianism, and I don’t intend to change that, but, again, how integrate this into my life? Can I really tell myself part of the Jewish people even if only one great-grand parent out of 8 was Jew? As I understand, I am “legally” a Jew, do I have some duties or rights in that regard? Incidentally, I took a module of Hebrew at university since september and am now able to read it. I feel like many things got in place knowing those origins, my interest in judaism, hebrew language, and Israël finally make sense.