No. That wasn't Fernand's fault at all. Old Dantes was a proud man, and didn't want to accept help from anyone. Mercedes even wanted him to live with her so she could take care of him, but the old man refused. He became a hermit and stopped eating. Mercedes recruited the senior Morrel to help, but old Dantes insisted on isolating himself until he died of starvation.

Old Dantes had an inkling that he'd never see Edmond again, and willed himself to death.

I’ve forgotten whether that was stated, but it certainly wouldn’t surprise me.