In recent years, Transformer-based models such as the Switch Transformer have achieved remarkable results in natural language processing tasks. However, these models are often too complex and require extensive pre-training, which limits their effectiveness for small clinical text classification tasks with limited data. In this study, we propose a simplified Switch Transformer framework and train it from scratch on a small French clinical text classification dataset at CHU Sainte-Justine hospital. Our results demonstrate that the simplified small-scale Transformer models outperform pre-trained BERT-based models, including DistillBERT, CamemBERT, FlauBERT, and FrALBERT. Additionally, using a mixture of expert mechanisms from the Switch Transformer helps capture diverse patterns; hence, the proposed approach achieves better results than a conventional Transformer with the self-attention mechanism. Finally, our proposed framework achieves an accuracy of 87\%, precision at 87\%, and recall at 85\%, compared to the third-best pre-trained BERT-based model, FlauBERT, which achieved an accuracy of 84\%, precision at 84\%, and recall at 84\%. However, Switch Transformers have limitations, including a generalization gap and sharp minima. We compare it with a multi-layer perceptron neural network for small French clinical narratives classification and show that the latter outperforms all other models.