Unless Google wants do withdraw its business from France and potentially all Europe, it will comply. I think it is quite probable it will comply, it is in its financial interests.
"Right to be forgotten" is a euphemism for censorship, and censorship is anathema to the Internet. That's the beginning and end of the matter. Stop legislating fantasies.
The reason someone's search results are considered 'objectionable' is because they consider those results private. The private citizen, in the case, is the censor. The french government is just the enforcing body behind that censorship.