Temporal language grounding (TLG) aims to localize a video segment in an untrimmed video based on a natural language description. To alleviate the expensive cost of manual annotations for temporal boundary labels,we are dedicated to the weakly supervised setting, where only video-level descriptions are provided for training. Most of the existing weakly supervised methods generate a candidate segment set and learn cross-modal alignment through a MIL-based framework. However, the temporal structure of the video as well as the complicated semantics in the sentence are lost during the learning. In this work, we propose a novel candidate-free framework: Fine-grained Semantic Alignment Network (FSAN), for weakly supervised TLG. Instead of view the sentence and candidate moments as a whole, FSAN learns token-by-clip cross-modal semantic alignment by an iterative cross-modal interaction module, generates a fine-grained cross-modal semantic alignment map, and performs grounding directly on top of the map. Extensive experiments are conducted on two widely-used benchmarks: ActivityNet-Captions, and DiDeMo, where our FSAN achieves state-of-the-art performance.