Translating wordplay across languages presents unique challenges that have long confounded both professional human translators and machine translation systems. This research proposes a novel approach for translating puns from English to French by combining state-of-the-art large language models with specialized techniques for wordplay generation. Our methodology employs a three-stage approach. First, we establish a baseline using multiple frontier large language models with feedback based on a new contrastive learning dataset. Second, we implement a guided chain-of-thought pipeline with combined phonetic-semantic embeddings. Third, we implement a multi-agent generator-discriminator framework for evaluating and regenerating puns with feedback. Moving beyond the limitations of literal translation, our methodology's primary objective is to capture the linguistic creativity and humor of the source text wordplay, rather than simply duplicating its vocabulary. Our best runs earned first and second place in the CLEF JOKER 2025 Task 2 competition where they were evaluated manually by expert native French speakers. This research addresses a gap between translation studies and computational linguistics by implementing linguistically-informed techniques for wordplay translation, advancing our understanding of how language models can be leveraged to handle the complex interplay between semantic ambiguity, phonetic similarity, and the implicit cultural and linguistic awareness needed for successful humor.