Censor: to examine in order to suppress or delete anything considered objectionable.

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.

You are using a general definition "removing objectionable information" here but most people, when reading "censorship" will understand it refers to a different concept like "deplorable practice of suppressing communication between people by force". You cannot, in general, put personal information regarding an individual in place of that communication and call exercising right to control personal data censorship. The right to be forgotten does not mean anything objectionable can be removed and it does not apply to public figures, companies or corporations. It only applies to individuals and search queries containing their name. In special cases the objected search result is important to the public, the right to be forgotten does not apply. So no, it is not censorship.