Each map has its own database collection from which it fetches data. You can access this data in its entirety using the api, which will return it the data in JSON format in the browser. JSON format is not very readable like tabular data, but you can convert it to a CSV format by copying the data from the browser and using a website such as data.page or anyconv.com.
Similarly, you can fetch the data directly into your own project, but I do ask that you only do so in a development or sandbox environment and not production. Throughput costs money. If you do want to use this data in your own project, feel free to updload it to your own database, or place it in a raw file on GitHub to serve it to your project. Also, make sure to credit Mapping French Diplomacy for the data.
Below you will find the api routes for each dataset.
Cite this page:
Nathan Michalewicz, “Technology Stack,” in Mappping French Diplomacy: Royal Correspondence and Diplomatic Geography 1494-1715. https://mappingfrenchdiplomacy.org/appendix/data