Cued Speech is a communication system developed for deaf people to complement speechreading at the phonetic level with hands. This visual communication mode uses handshapes in different placements near the face in combination with the mouth movements of speech to make the phonemes of spoken language look different from each other. This paper describes CLeLfPC - Corpus de Lecture en Langue française Parlée Complétée, a corpus of French Cued Speech. It consists in about 4 hours of audio and HD video recordings of 23 participants. The recordings are 160 different isolated ‘CV’ syllables repeated 5 times, 320 words or phrases repeated 2-3 times and about 350 sentences repeated 2-3 times. The corpus is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License. It can be used for any further research or teaching purpose. The corpus includes orthographic transliteration and other phonetic annotations on 5 of the recorded topics, i.e. syllables, words, isolated sentences and a text. The early results are encouraging: it seems that 1/ the hand position has a high influence on the key audio duration; and 2/ the hand shape has not.