Blind face restoration (BFR) aims to recover high-quality facial images from degraded inputs, yet its inherently ill-posed nature leads to ambiguous and uncontrollable solutions. Recent diffusion-based BFR methods improve perceptual quality but remain uncontrollable, whereas text-guided face editing enables attribute manipulation without reliable restoration. To address these issues, we propose A$^2$BFR, an attribute-aware blind face restoration framework that unifies high-fidelity reconstruction with prompt-controllable generation. Built upon a Diffusion Transformer backbone with unified image-text cross-modal attention, A$^2$BFR jointly conditions the denoising trajectory on both degraded inputs and textual prompts. To inject semantic priors, we introduce attribute-aware learning, which supervises denoising latents using facial attribute embeddings extracted by an attribute-aware encoder. To further enhance prompt controllability, we introduce semantic dual-training, which leverages the pairwise attribute variations in our newly curated AttrFace-90K dataset to enforce attribute discrimination while preserving fidelity. Extensive experiments demonstrate that A$^2$BFR achieves state-of-the-art performance in both restoration fidelity and instruction adherence, outperforming diffusion-based BFR baselines by -0.0467 LPIPS and +52.58% attribute accuracy, while enabling fine-grained, prompt-controllable restoration even under severe degradations.