The successes of contextual word embeddings learned by training large-scale language models, while remarkable, have mostly occurred for languages where significant amounts of raw texts are available and where annotated data in downstream tasks have a relatively regular spelling. Conversely, it is not yet completely clear if these models are also well suited for lesser-resourced and more irregular languages. We study the case of Old French, which is in the interesting position of having relatively limited amount of available raw text, but enough annotated resources to assess the relevance of contextual word embedding models for downstream NLP tasks. In particular, we use POS-tagging and dependency parsing to evaluate the quality of such models in a large array of configurations, including models trained from scratch from small amounts of raw text and models pre-trained on other languages but fine-tuned on Medieval French data.