This paper describes a system for interactive poem generation, which combines neural language models (LMs) for poem generation with explicit constraints that can be set by users on form, topic, emotion, and rhyming scheme. LMs cannot learn such constraints from the data, which is scarce with respect to their needs even for a well-resourced language such as French. We propose a method to generate verses and stanzas by combining LMs with rule-based algorithms, and compare several approaches for adjusting the words of a poem to a desired combination of topics or emotions. An approach to automatic rhyme setting using a phonetic dictionary is proposed as well. Our system has been demonstrated at public events, and log analysis shows that users found it engaging.