De novo drug design is a crucial component of modern drug development, yet navigating the vast chemical space to find synthetically accessible, high-affinity candidates remains a significant challenge. Reinforcement Learning (RL) enhances this process by enabling multi-objective optimization and exploration of novel chemical space - capabilities that traditional supervised learning methods lack. In this work, we introduce \textbf{ReACT-Drug}, a fully integrated, target-agnostic molecular design framework based on Reinforcement Learning. Unlike models requiring target-specific fine-tuning, ReACT-Drug utilizes a generalist approach by leveraging ESM-2 protein embeddings to identify similar proteins for a given target from a knowledge base such as Protein Data Base (PDB). Thereafter, the known drug ligands corresponding to such proteins are decomposed to initialize a fragment-based search space, biasing the agent towards biologically relevant subspaces. For each such fragment, the pipeline employs a Proximal Policy Optimization (PPO) agent guiding a ChemBERTa-encoded molecule through a dynamic action space of chemically valid, reaction-template-based transformations. This results in the generation of \textit{de novo} drug candidates with competitive binding affinities and high synthetic accessibility, while ensuring 100\% chemical validity and novelty as per MOSES benchmarking. This architecture highlights the potential of integrating structural biology, deep representation learning, and chemical synthesis rules to automate and accelerate rational drug design. The dataset and code are available at https://github.com/YadunandanRaman/ReACT-Drug/.