Inclusive French (gender-neutral language) is a variety of French that is used to highlight awareness of gender and identity against Standard French, which enforces the use of masculine for generic usage or plural. Although widely used and challenging to a set of NLP tools, Inclusive French was very little studied in NLP. Detractors of Inclusive French argue that it is difficult to read, while its supporters argue that it provides a fairer representation of women and gender minorities. We provide INCLURE, the first large-scale parallel corpus for Standard to Inclusive French translation, and vice-versa, thus providing a "bilingual" access to French, for both detractors and supporters of Inclusive French. This corpus comes with a toolkit that can be readily applied to larger French corpora and could be extended to other languages, for which the number of inclusive varieties is growing. We also provide Fabien.ne BARThez, a sequence-to-sequence model trained on INCLURE. Apart from its direct application to translation, this model could also be used in most NLP pipelines, either as a pre-processing step to improve downstream processing or as a post-processing according to the user's preference.