Let's get a useful tip out of the way first:
If you can't send and/or receive GMX emails via whichever email app you use on your iPad, you've always got a back-up plan available to you:
Simply launch your web browser (which will be Safari unless you've installed something else), go to
https://www.gmx.co.uk and log into your email account there. That does away with the need to worry about things like SMTP servers (which is what's been causing your problems), so you'll ALWAYS be able to access your emails. (i.e. as long as you had internet access, you should always have been able to send and receive emails in France by that method).
Your iPad comes with a dedicated email app on it, simply called 'Mail'. There's no real reason why you shouldn't use it with
any email service but it often makes most sense to use an app that's specifically designed to pair up with your own email service. i.e. if you're not already using it, you might want to consider installing GMX's own dedicated app:
https://itunes.apple.com/gb/app/gmx-mail/id417352269?mt=8
(I use the Android equivalent of it on my own phone)
If you use GMX's own app you should find that everything (including the all-important 'SMTP' and 'authentication' settings) is already set up for you.
Otherwise, if you're using the default Mail app on your iPad, you'll need to go into its settings for your account. (See 'Check your settings' here:
https://support.apple.com/en-gb/ht201419 ). You'll then need to check that the 'outgoing' ('SMTP') settings match those given here:
https://support.gmx.com/pop-imap/imap/server.html
That should fix your problem but, if all else fails, simply delete your GMX account on your iPad and then create it again. (That will almost certainly work but you might find that hundreds, or even thousands, of old mails then get downloaded to your iPad!)