Thanks for your message, here are a few answers.

Type of connection : wired
Other programs running : steam, usually also firefox
Frequency : used to be really rare and fixed after one relaunch, but since today it's all the time

What I've done to try to resolve the issue : I changed DNS but that seems to have triggered account protection and I've been asked to change my password
I've tried deleting the launcher config file or editing it changing the browser setting but that didn't help

I was able to log in after going into config and reseting system settings but that looks like it was a fluke as after I've logged out I still have the same problem.

I did now tweak the internet explorer options as described, and restarted PC, but the problem was still there afterwards though now I sometimes have other script errors displayed

"An error occured on a script for this page

line : 114
caracter : 2
Error : "swk" is undefined
Code : 0
URL : https://ffxiv-login.square-enix.com/...ft=0&issteam=1

Do you still wish to excute scripts on this page ? Yes / No"

I will try again after resetting my router.