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For soft robots to work effectively in human-centered environments, they need to be able to estimate their state and external interactions based on (proprioceptive) sensors. Estimating disturbances allows a soft robot to perform desirable force control. Even in the case of rigid manipulators, force estimation at the end-effector is seen as a non-trivial problem. And indeed, other current approaches to address this challenge have shortcomings that prevent their general application. They are often based on simplified soft dynamic models, such as the ones relying on a piece-wise constant curvature (PCC) approximation or matched rigid-body models that do not represent enough details of the problem. Thus, the applications needed for complex human-robot interaction can not be built. Finite element methods (FEM) allow for predictions of soft robot dynamics in a more generic fashion. Here, using the soft robot modeling capabilities of the framework SOFA, we build a detailed FEM model of a multi-segment soft continuum robotic arm composed of compliant deformable materials and fiber-reinforced pressurized actuation chambers with a model for sensors that provide orientation output. This model is used to establish a state observer for the manipulator. Model parameters were calibrated to match imperfections of the manual fabrication process using physical experiments. We then solve a quadratic programming inverse dynamics problem to compute the components of external force that explain the pose error. Our experiments show an average force estimation error of around 1.2%. As the methods proposed are generic, these results are encouraging for the task of building soft robots exhibiting complex, reactive, sensor-based behavior that can be deployed in human-centered environments.