Your steps worked to update the one incompatible widget. I used these steps:
1) Finish the translation of a page
2) Ensure that language in top header is your default one
3) When publishing on the right side there is a switch "Use WPML's Translation Editor" , se to off
4) Click to translate the page in the language you wish
5) You will not see WPML Translation Editor. Please replace the link ( only the link please do not touch anything else )
6) Switch again to the default language in the top bar
7) Enabled again WPML TRanslation editor.
However, for another widget - the footer which goes across all pages, it does not work. I have amended the translation in "string translate" - see screenshot 1. It does not update though. I tried to use the steps above for the footer, but I only see the English text, not the french text. Please see screenshot 2.
Also as far as I can see you are using Organic Customizer Widgets for widgets. If yes, then as far as I can see we are not having any compatibility with that plugin, so very likely this is the reason it is not working.
Since you are using it, please try to use the default widgets of WP instead in order to see if everything is working ok.
On the other hand, I am wrong about the above and you are using the default way, please share a screencast of the problem.
Regards,
Andreas
This ticket is now closed. If you're a WPML client and need related help, please open a new support ticket.