Domain mapping Cookie

hi
I am in desperate needs of someone help to make my project moving
I have a website http://www.myfrenchcity.com with multiple subdomain and outside domain like http://www.exemple.com on the same mapping
i need to access all domain with remote login but i can not
it seems i have a cookie pb but i can not find where it is I have checked the wp-config

on wpmu dashboad i can see COOKIE_DOMAIN .myfrenchcity.com

i do not know what to do I have disable all the plugin ecept ultimate branding
let me know if someone can assist me in setting up correctly

Regards

https://ww.wp.xz.cn/plugins/wordpress-mu-domain-mapping/