My mom grew up calling her grandmother “Citie” (I’m not sure if that’s how it’s spelled) and she thinks it was French. Is this actually the sound of a French word? I haven’t been able to find “citie” online anywhere. It doesn’t sound anything like “grand-mere.”
Citie doesn't sound like any of the common nicknames used by grandchildren to call their grandmothers.
Here is a poll that says that among the 617 families who answered, 208 different ones were used. That's quite a lot.
There is titi in the list. It is a common nickname in France, although not specifically for a grandmother. That or titie might be what your mother used anyway, especially if her grandmother's first name contained t or ti.