Many studies have shown that transformers are able to predict subject-verb agreement, demonstrating their ability to uncover an abstract representation of the sentence in an unsupervised way. Recently, Li et al. (2021) found that transformers were also able to predict the object-past participle agreement in French, the modeling of which in formal grammar is fundamentally different from that of subject-verb agreement and relies on a movement and an anaphora resolution. To better understand transformers’ internal working, we propose to contrast how they handle these two kinds of agreement. Using probing and counterfactual analysis methods, our experiments on French agreements show that (i) the agreement task suffers from several confounders that partially question the conclusions drawn so far and (ii) transformers handle subject-verb and object-past participle agreements in a way that is consistent with their modeling in theoretical linguistics.