It is possible if you export from the correct context. If you have this relationship:
you'll want to export records from the ChildTable, but include the fields that you need from ParentTable as part of the data export.
If you are doing this manually, by selecting export records from the File Menu, start from a layout based on the ChildTable.
Can you be more precise because it's someone else who builted the linked tables for me and I am not tough in FMP
I am French too... ( the English forum seems to be much more reactive than the french one...)
I can't be more precise as I do not know the structure of the tables you want to use to produce this csv file. You'll need to describe the tables and relationships involved.