Contact-rich manipulation requires robots to continuously perceive and regulate evolving physical interactions under dynamic contact transitions or complex surface geometries. Recent imitation learning methods improve contact-aware control by incorporating tactile or force feedback, but they rarely model the asymmetric spatiotemporal roles of global force and local tactile sensing. To address this, we propose TacForeSight, a lightweight force-conditioned tactile foresight framework for real-time manipulation. The core component is TacForceWM, a tactile world model that predicts short-horizon tactile latent dynamics from dual-finger tactile observations conditioned on high-frequency wrist force and torque signals. Another key component, the Predictive Tactile-Conditioned Policy, leverages the predicted latents as anticipatory contact priors, models the current-to-future tactile evolution via cross-attention, and adaptively fuses visuo-tactile features through a tactile-guided gating module. By forecasting purely within a compact latent space, TacForeSight enables proactive contact reasoning with efficient real-time inference suitable for high-frequency manipulation control. Real-robot experiments on five representative tasks and three in-process perturbation settings show that TacForeSight consistently outperforms existing baselines, particularly under dynamic contact disturbances. All models and datasets will be made publicly available on the project website at https://tacforesight.github.io/ProjectPage.