You have read the FUD:
- You will have to spend a lot to migrate to GNU/Linux
- You will need some particular app not available on GNU/Linux
- You will not save any money
- TCO higher with GNU/Linux
- etc.
Well, it is not true. You can do it. Here’s how the French police did it.
- wake up to the reality of the Wintel treadmill
- wake up to the reality of the cash flow to licensing
- choose to use FLOSS apps
- when all the FLOSS works and you use the browser for apps on the server, change the OS
- because your users are used to the FLOSS apps, there is only a small cost to migrating the OS.
They saved millions of Euros over several years with this approach. In a few years 100000 employees will be free of that other OS completely.
This is a recipe that works, but I still like making the switch on a weekend. 
Earlier this morning I clicked on the link you provided and was greeted with this:
This Sunday afternoon we are going to do some maintenance tasks in the platform and the services will be totally stopped during the maintenance window.
The platform will be unaccessible from 17:30 to 21:00.
Sorry for any inconvenience, the OSOR team.
That’s not exactly a great endorsement. Running Linux requires maintenance so severe you have to stop serving web pages? They don’t seem to know what they are doing, quite frankly.
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Your comment assumes that running GNU/Linux required serious downtime. It is their business what service level they want to run. If they felt it was important not to have an outage they could have switched to another server for surgery. I really do not care. Netcraft reports some seriously reliable sites running GNU/Linux.