Soft grippers display adaptability, dexterity, and safety, garnering increased interest in their applications. However, accurately modeling their nonlinear deformation and sensing the grasping force remain challenging. Here, a generalized closed-form kinetostatic model of a biomimetic FRE soft finger is established based on the chained-beam-constraint model. A methodology combining a geometry-based contact constraint technique is presented, utilizing the minimum strain energy principle for sensorless, precise, and rapid estimation of the deformed contours and contact force when the FRE finger grasps an arbitrary object with a continuous surface. Method verification using FEA demonstrates a maximum error of no more than 1.28% and 2.44% for the contour and contact force estimation, respectively. Subsequently, a multiobjective genetic algorithm is used to optimize the FRE finger design for better adaptability and greater grasping force in a special scenario. Finally, the finger's capability to accurately perceive grasping force and deformed contours was demonstrated by four groups of grasping tests using cylinder and cube objects, with maximum average absolute error and relative error of 0.083 N, 9.84%, and 1.335 mm, 10.06%, respectively.