Self-Supervised Learning (SSL) using huge unlabeled data has been successfully explored for image and natural language processing. Recent works also investigated SSL from speech. They were notably successful to improve performance on downstream tasks such as automatic speech recognition (ASR). While these works suggest it is possible to reduce dependence on labeled data for building efficient speech systems, their evaluation was mostly made on ASR and using multiple and heterogeneous experimental settings (most of them for English). This questions the objective comparison of SSL approaches and the evaluation of their impact on building speech systems. In this paper, we propose LeBenchmark: a reproducible framework for assessing SSL from speech. It not only includes ASR (high and low resource) tasks but also spoken language understanding, speech translation and emotion recognition. We also focus on speech technologies in a language different than English: French. SSL models of different sizes are trained from carefully sourced and documented datasets. Experiments show that SSL is beneficial for most but not all tasks which confirms the need for exhaustive and reliable benchmarks to evaluate its real impact. LeBenchmark is shared with the scientific community for reproducible research in SSL from speech.