Self-supervised learning (SSL) is at the origin of unprecedented improvements in many different domains including computer vision and natural language processing. Speech processing drastically benefitted from SSL as most of the current domain-related tasks are now being approached with pre-trained models. This work introduces LeBenchmark 2.0 an open-source framework for assessing and building SSL-equipped French speech technologies. It includes documented, large-scale and heterogeneous corpora with up to 14,000 hours of heterogeneous speech, ten pre-trained SSL wav2vec 2.0 models containing from 26 million to one billion learnable parameters shared with the community, and an evaluation protocol made of six downstream tasks to complement existing benchmarks. LeBenchmark 2.0 also presents unique perspectives on pre-trained SSL models for speech with the investigation of frozen versus fine-tuned downstream models, task-agnostic versus task-specific pre-trained models as well as a discussion on the carbon footprint of large-scale model training. Overall, the newly introduced models trained on 14,000 hours of French speech outperform multilingual and previous LeBenchmark SSL models across the benchmark but also required up to four times more energy for pre-training.