My cousin passed away. She was married but separated from her spouse. She had no children, no siblings and her parents passed away as well. In her will, she bequeathed all of her real estate to me. My notary tells me that if I give up (...)

...  her property will revert to her spouse. Is it correct?

Yes. Renunciation of a bequest has the effect of rendering the testamentary disposition null and void (art. 1043 C. civ.). The devolution of inheritance then takes place as if this provision had never existed. Since your cousin has no descendants, her father and mother having passed away, the inheritance is collected in its entirety by the spouse (art. 757-2 C. civ.), even though they were separated, provided that they were still married (art. 732 C. civ.).

This solution would have been different if your cousin had appointed a second legatee.

Please note: in the absence of children, the spouse is reserved for 1/4 of the assets of the inheritance.