In the rapidly evolving field of vision-language navigation (VLN), ensuring safety for physical agents remains an open challenge. For a human-in-the-loop language-operated drone to navigate safely, it must understand natural language commands, perceive the environment, and simultaneously avoid hazards in real time. Control Barrier Functions (CBFs) are formal methods that enforce safe operating conditions. Model Predictive Control (MPC) is an optimization framework that plans a sequence of future actions over a prediction horizon, ensuring smooth trajectory tracking while obeying constraints. In this work, we consider a VLN-operated drone platform and enhance its safety by formulating a novel scene-aware CBF that leverages ego-centric observations from a camera which has both Red-Green-Blue as well as Depth (RGB-D) channels. A CBF-less baseline system uses a Vision-Language Encoder with cross-modal attention to convert commands into an ordered sequence of landmarks. An object detection model identifies and verifies these landmarks in the captured images to generate a planned path. To further enhance safety, an Adaptive Safety Margin Algorithm (ASMA) is proposed. ASMA tracks moving objects and performs scene-aware CBF evaluation on-the-fly, which serves as an additional constraint within the MPC framework. By continuously identifying potentially risky observations, the system performs prediction in real time about unsafe conditions and proactively adjusts its control actions to maintain safe navigation throughout the trajectory. Deployed on a Parrot Bebop2 quadrotor in the Gazebo environment using the Robot Operating System (ROS), ASMA achieves 64%-67% increase in success rates with only a slight increase (1.4%-5.8%) in trajectory lengths compared to the baseline CBF-less VLN.