Named Entity Recognition (NER) involves the identification and classification of named entities in unstructured text into predefined classes. NER in languages with limited resources, like French, is still an open problem due to the lack of large, robust, labelled datasets. In this paper, we propose a transformer-based NER approach for French using adversarial adaptation to similar domain or general corpora for improved feature extraction and better generalization. We evaluate our approach on three labelled datasets and show that our adaptation framework outperforms the corresponding non-adaptive models for various combinations of transformer models, source datasets and target corpora.