Despite being a non-invasive imaging modality, coronary computed tomography angiography (CCTA) is still not the clinical gold-standard modality for the diagnosis and evaluation of Coronary Artery Diseases (CAD), which is typically performed with an invasive coronary angiography (ICA). In this work, we aim at bringing CCTA diagnosis performance closer to the level of the ICA. We propose a deep attention learning framework that takes as an input non-invasive CCTA images and is able to predict a clinical decision, such as revascularization, that is typically based on invasive modalities such as ICA. We represent the CCTA volumetric imaging by two cross-sectional views that follow the curvature of the coronary artery, and we use an attention mechanism that learns a fused representation for better diagnosis. Experimental results on a clinical study of 80 patients indicate that the learned fused model achieves a significant gain in the performance (F1-score: 0.53 +- 0.11) with respect to the CT fractional-flow-reserve (FFR_CT), a clinical baseline estimating the drop of flow from CCTA (F1-score: 0.46+-0.09). These preliminary results confirm that a data-driven approach can boost the diagnosis power of CCTA and eventually contribute towards the wider adoption of this non-invasive imaging modality in clinical settings.