Micro-scale continuum robots face significant limitations in achieving three-dimensional contact force perception, primarily due to structural miniaturization, nonlinear mechanical, and sensor integration. To overcome these limitations, this paper introduces a novel proprioception method for cable-driven continuum robots based on proximal-integrated force sensing (i.e., cable tension and six-axis force/torque (F/T) sensor), inspired by the tendon-joint collaborative sensing mechanism of the finger. By integrating biomechanically inspired design principles with nonlinear modeling, the proposed method addresses the challenge of force perception (including the three-dimensional contact force and the location of the contact point) and shape estimation in micro-scale continuum robots. First, a quasi-bionic mapping between human tissues/organs and robot components is established, enabling the transfer of the integrated sensing strategy of tendons, joints, and neural feedback to the robotic system. Second, a multimodal perception strategy is developed based on the structural constraints inherent to continuum robots. The complex relationships among mechanical and material nonlinearities, robot motion states, and contact forces are formulated as an optimization problem to reduce the perception complexity. Finally, experimental validation demonstrates the effectiveness of the proposed method. This work lays the foundation for developing safer and smarter continuum robots, enabling broader clinical adoption in complex environments.