Floor plans can provide valuable prior information that helps enhance the accuracy of indoor positioning systems. However, existing research typically faces challenges in efficiently leveraging floor plan information and applying it to complex indoor layouts. To fully exploit information from floor plans for positioning, we propose a floor plan-assisted fusion positioning algorithm (FP-BP) using Bluetooth low energy (BLE) and pedestrian dead reckoning (PDR). In the considered system, a user holding a smartphone walks through a positioning area with BLE beacons installed on the ceiling, and can locate himself in real time. In particular, FP-BP consists of two phases. In the offline phase, FP-BP programmatically extracts map features from a stylized floor plan based on their binary masks, and constructs a mapping function to identify the corresponding map feature of any given position on the map. In the online phase, FP-BP continuously computes BLE positions and PDR results from BLE signals and smartphone sensors, where a novel grid-based maximum likelihood estimation (GML) algorithm is introduced to enhance BLE positioning. Then, a particle filter is used to fuse them and obtain an initial estimate. Finally, FP-BP performs post-position correction to obtain the final position based on its specific map feature. Experimental results show that FP-BP can achieve a real-time mean positioning accuracy of 1.19 m, representing an improvement of over 28% compared to existing floor plan-fused baseline algorithms.