Designing analog circuits from performance specifications is a complex, multi-stage process encompassing topology selection, parameter inference, and layout feasibility. We introduce FALCON, a unified machine learning framework that enables fully automated, specification-driven analog circuit synthesis through topology selection and layout-constrained optimization. Given a target performance, FALCON first selects an appropriate circuit topology using a performance-driven classifier guided by human design heuristics. Next, it employs a custom, edge-centric graph neural network trained to map circuit topology and parameters to performance, enabling gradient-based parameter inference through the learned forward model. This inference is guided by a differentiable layout cost, derived from analytical equations capturing parasitic and frequency-dependent effects, and constrained by design rules. We train and evaluate FALCON on a large-scale custom dataset of 1M analog mm-wave circuits, generated and simulated using Cadence Spectre across 20 expert-designed topologies. Through this evaluation, FALCON demonstrates >99\% accuracy in topology inference, <10\% relative error in performance prediction, and efficient layout-aware design that completes in under 1 second per instance. Together, these results position FALCON as a practical and extensible foundation model for end-to-end analog circuit design automation.