Possible Clues:

• French writer and philosopher
• He wrote 'I exist, that is all, and I find it nauseating'
• Rarest sort of philosopher
• Writer's skill showcased in series regularly
• Arrest bully with French philosopher
• 1964 Nobel Prize refuser
• Jean-Paul --, French philosopher, novelist, and dramatist
• A writer regularly dividing extremists in Sorbonne?
• "Being and Nothingness" author Jean-Paul
• “No Exit” playwright