The task of Named Entity Recognition (NER) is central for leveraging the content of clinical texts in observational studies. Indeed, texts contain a large part of the information available in Electronic Health Records (EHRs). However, clinical texts are highly heterogeneous between healthcare services and institutions, between countries and languages, making it hard to predict how existing tools may perform on a particular corpus. We compared four NER approaches on three French corpora and share our benchmarking pipeline in an open and easy-to-reuse manner, using the medkit Python library. We include in our pipelines fine-tuning operations with either one or several of the considered corpora. Our results illustrate the expected superiority of language models over a dictionary-based approach, and question the necessity of refining models already trained on biomedical texts. Beyond benchmarking, we believe sharing reusable and customizable pipelines for comparing fast-evolving Natural Language Processing (NLP) tools is a valuable contribution, since clinical texts themselves can hardly be shared for privacy concerns.