Frontier artificial intelligence is reshaping all aspects of society, from economic output or military capability to democratic institutions. The EU is entering this transformation from a position of structural dependence: frontier models originate almost exclusively from the United States or China, the US holds approximately sixteen times the EU's AI supercomputing capacity, and only 15% of global hyperscale data centre capacity resides within EU borders. Although the European Commission has accelerated its policy response, existing initiatives remain fragmented and lack a cohesive vision for securing strategic autonomy across the full frontier AI value chain. Here we propose a unified framework connecting five sovereignty pillars (economic competitiveness, resilience, security and defence, European values, and foreign relations) to a decomposition of the frontier AI stack comprising five layers, 26 components, and 29 sub-components. This framework allows the identification of critical gaps, redundancies, and inter-pillar trade-offs that current EU policy leaves implicit. Our analysis of the AI Gigafactory Initiative illustrates how a sovereignty-centred lens reveals conflicts that narrowly economic framings obscure. Moreover, this framework offers policymakers a structured basis for designing, evaluating, and prioritising frontier AI interventions across multiple dimensions of European strategic autonomy across the 92 initiatives from four major Commission communications we. identify, and beyond.