Vincent Pradeilles presented on advanced functional programming at CocoaHeads Lyon, focusing on practical use cases for monads and illustrating concepts like pure functions, optionals, and function composition. He introduced the idea of monads as a way to wrap types inside contexts and facilitate workflows, showcasing a 'writer monad' for tracking computation logs. The session concluded with architectural models for managing application state and actions in a functional programming style, highlighting the advantages and challenges of these approaches.