Hi there,
I'm Cherrelyn and I'm here to help.
Please try removing the account from Outlook.com and then adding it back using your most recent email password. Make sure to use the correct server settings from Orange’s support page. Once it reconnects, your emails should sync again so you can properly compare it with the Outlook desktop app.
I hope this will help and If you have any question please feel free to ask.
Warm regards,
Cherrelyn