Tennis match analysis and tactical recommendation remain challenging due to the lack of structured, machine-readable representations that capture high-level spatial and strategic dynamics. Most existing AI-based approaches rely on unstructured textual descriptions or coarse-grained statistics, which limits their ability to support fine-grained tactical reasoning and actionable decision support. In this paper, we propose TANS-Agent, a multi-agent AI framework that leverages the Tennis Algebraic Notation System (TANS) to enable structured and interpretable tennis analysis. By using TANS as a unified high-level representation, TANS-Agent grounds Large Language Model (LLM) agents in explicit spatial and tactical semantics and supports statistical analysis, spatial pattern discovery, and tactical reasoning within a staged multi-agent pipeline. Due to the limited availability of fully structured match data, we study six professional matches between Qinwen Zheng and Aryna Sabalenka, which are manually charted into TANS. We systematically compare three types of input data—web-based match descriptions, TennisAbstract-based data, and TANS-based representations—and show that increased levels of tactical structure and spatial precision lead to more interpretable, consistent, and tactically grounded strategy recommendations.