Vision-language foundation models such as CLIP have shown impressive zero-shot performance on many tasks and datasets, especially thanks to their free-text inputs. However, they struggle to handle some downstream tasks, such as fine-grained attribute detection and localization. In this paper, we propose a multitask fine-tuning strategy based on a positive/negative prompt formulation to further leverage the capacities of the vision-language foundation models. Using the CLIP architecture as baseline, we show strong improvements on bird fine-grained attribute detection and localization tasks, while also increasing the classification performance on the CUB200-2011 dataset. We provide source code for reproducibility purposes: it is available at https://github.com/FactoDeepLearning/MultitaskVLFM.