(1) Background: Epi- and Paracardial Adipose Tissue (EAT, PAT) have been spotlighted as important biomarkers in cardiological assessment in recent years. Since biomarker quantification is an increasingly important method for clinical use, we wanted to examine fully automated EAT and PAT quantification for possible use in cardiovascular risk stratification. (2) Methods: 966 patients with intermediate Framingham risk scores for Coronary Artery Disease referred for coronary calcium scans were included in clinical routine retrospectively. The Coronary Artery Calcium Score (CACS) was extracted and tissue quantification was performed by a deep learning network. (3) Results: The Computed Tomography (CT) segmentations predicted by the network indicated no significant correlation between EAT volume and EAT radiodensity when compared to Agatston score (r = 0.18, r = −0.09). CACS 0 category patients showed significantly lower levels of total EAT and PAT volumes and higher EAT and PAT densities than CACS 1–99 category patients (p < 0.01). Notably, this difference did not reach significance regarding EAT attenuation in male patients. Women older than 50 years, thus more likely to be postmenopausal, were shown to be at higher risk of coronary calcification (p < 0.01, OR = 4.59). CACS 1–99 vs. CACS ≥100 category patients remained below significance level (EAT volume: p = 0.087, EAT attenuation: p = 0.98). (4) Conclusions: Our study proves the feasibility of a fully automated adipose tissue analysis in clinical cardiac CT and confirms in a large clinical cohort that volume and attenuation of EAT and PAT are not correlated with CACS. Broadly available deep learning based rapid and reliable tissue quantification should thus be discussed as a method to assess this biomarker as a supplementary risk predictor in cardiac CT.