The casual, neutral, and formal language registers are highly perceptible in discourse productions. However, they are still poorly studied in Natural Language Processing (NLP), especially outside English, and for new textual types like tweets. To stimulate research, this paper introduces a large corpus of 228,505 French tweets (6M words) annotated in language registers. Labels are provided by a multi-label CamemBERT classifier trained and checked on a manually annotated subset of the corpus, while the tweets are selected to avoid undesired biases. Based on the corpus, an initial analysis of linguistic traits from either human annotators or automatic extractions is provided to describe the corpus and pave the way for various NLP tasks. The corpus, annotation guide and classifier are available on http://tremolo.irisa.fr.