Assessing the severity of stenoses in coronary angiography is critical to the patient's health, as coronary stenosis is an underlying factor in heart failure. Current practice for grading coronary lesions, i.e. fractional flow reserve (FFR) or instantaneous wave-free ratio (iFR), suffers from several drawbacks, including time, cost and invasiveness, alongside potential interobserver variability. In this context, some deep learning methods have emerged to assist cardiologists in automating the estimation of FFR/iFR values. Despite the effectiveness of these methods, their reliance on large datasets is challenging due to the distributed nature of sensitive medical data. Federated learning addresses this challenge by aggregating knowledge from multiple nodes to improve model generalization, while preserving data privacy. We propose the first federated detection transformer approach, FeDETR, to assess stenosis severity in angiography videos based on FFR/iFR values estimation. In our approach, each node trains a detection transformer (DETR) on its local dataset, with the central server federating the backbone part of the network. The proposed method is trained and evaluated on a dataset collected from five hospitals, consisting of 1001 angiographic examinations, and its performance is compared with state-of-the-art federated learning methods.