My mother has been in France for the past 15 years. I’m an Israeli citizen living in the US as a green card holder.
If I wanted to legally live in France and be with her is there anything that can be done? I’m in my 30s.
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Unfortunately, you need to be either younger than 21 years or dependent on your mother to qualify for a residence permit as the child of a French citizen. For example, the relevant page at service-public.fr includes (emphasis added):
famille d'un Français (époux d'un Français, parent d'un enfant français mineur vivant en France, enfant de moins de 21 ans ou à charge d'un Français, parents, grands-parents ou beaux-parents à charge d'un Français)
family of a French citizen (spouse of a French citizen, parent of a French minor living in France, child of less than 21 years or dependent on a French citizen, parents, grandparents or parents in law dependent on a French citizen)
Therefore, the answer to your question:
If I wanted to legally live in France and be with her is there anything that can be done?
You can use any of the other routes that are available to everyone, whether through work or as an "economically inactive" visitor.