The AppSheet app shows the label in the dropdown and saves the key of the parent table in the backend of the child table. Labels are more user friendly names and keys are cryptic many times.
If you wish to store the name of the client in the child table “FICHES PRODUIT” , you may do the following
Please create one additional column in the “FICHES PRODUIT” table and name this column as say [CLIENT KEY] . Please make this column as reference column that refers the CLIENTS table.
In the [ NOM DU CLIENT] column in the child table “FICHES PRODUIT” , please have app formula as [CLIENT KEY].[COLUMN NAME IN CLIENTS TABLE THAT CONTAINS CUSTOMER NAME]
This expression will pull the client name from the parent table “CLIENTS” and populate the [ NOM DU CLIENT] column in the child table. This expression and technique is called dereferencing.
Please do it with caution, just in case you have any other expressions/ columns based on the reference column in the child table.
Please go through below article and the sample app just in case you have not yet gone through
The sample app: