Floorplan reconstruction provides structural priors essential for reliable indoor robot navigation and high-level scene understanding. However, existing approaches either require time-consuming offline processing with a complete map, or rely on expensive sensors and substantial computational resources. To address the problems, we propose Floorplan-SLAM, which incorporates floorplan reconstruction tightly into a multi-session SLAM system by seamlessly interacting with plane extraction, pose estimation, and back-end optimization, achieving real-time, high-accuracy, and long-term floorplan reconstruction using only a stereo camera. Specifically, we present a robust plane extraction algorithm that operates in a compact plane parameter space and leverages spatially complementary features to accurately detect planar structures, even in weakly textured scenes. Furthermore, we propose a floorplan reconstruction module tightly coupled with the SLAM system, which uses continuously optimized plane landmarks and poses to formulate and solve a novel optimization problem, thereby enabling real-time incremental floorplan reconstruction. Note that by leveraging the map merging capability of multi-session SLAM, our method supports long-term floorplan reconstruction across multiple sessions without redundant data collection. Experiments on the VECtor and the self-collected datasets indicate that Floorplan-SLAM significantly outperforms state-of-the-art methods in terms of plane extraction robustness, pose estimation accuracy, and floorplan reconstruction fidelity and speed, achieving real-time performance at 25-45 FPS without GPU acceleration, which reduces the floorplan reconstruction time for a 1000 square meters scene from over 10 hours to just 9.44 minutes.