I have had a look. All the setup looks OK but as you say first time in a new tab the redirect is to the Home page but afterwards it is OK!!!
Think this is a Joomla Multi-language problem. It switches to the /fr home page first time. Suggest you try the Joomla! support forum as this is outside my experience.
PS Had one more go
If I go to site on a newbrowser tab and then click on English flag before
I login, then login on the Intranet page it takes me to the correct page with the Downloads on it. It was the french page of Downloads so maybe a mix up. For better checking out I would also suggest you change the menu names to include which language to see where one is during the devel.
So pretty sure it is a Joomla! multi language problem.