Video text detection (VTD) aims to localize text instances in videos, which has wide applications for downstream tasks. To deal with the variances of different scenes and text instances, multiple models and feature fusion strategies were typically integrated in existing VTD methods. A VTD method consisting of sophisticated components can efficiently improve detection accuracy, but may suffer from a limitation for real-time applications. This paper aims to achieve real-time VTD with an adaptive lightweight end-to-end framework. Different from previous methods that represent text in a spatial domain, we model text instances in the Fourier domain. Specifically, we propose a scale-aware Fourier Contour Embedding method, which not only models arbitrary shaped text contours of videos as compact signatures, but also adaptively select proper scales for features in a backbone in the training stage. Then, we construct VTD-FCENet to achieve real-time VTD, which encodes temporal correlations of adjacent frames with scale-aware FCE in a lightweight and adaptive manner. Quantitative evaluations were conducted on ICDAR2013 Video, Minetto and YVT benchmark datasets, and the results show that our VTD-FCENet not only obtains the state-of-the-arts or competitive detection accuracy, but also allows real-time text detection on HD videos simultaneously.