Please create a full backup of the database and website then go to WPML > Support > Troubleshooting page, and click the following:
- Clear the Cache in WPML
- Remove ghost entries from the translation tables
- Fix element_type collation
- Fix WPML table collation
- Set language information
- Fix post type assignment for translations
The "Delete selected strings" option in "String Translation" page will delete the French translation.
Please try the following steps and let us know how that goes:
- Go to WPML String Translation
- Delete the string
- Scroll down to the "Auto register strings for translation" section and enable that option
- Visit the page where the string is added on the front end
- Go back to String translation and disable the auto register option
- Search again for the string and translate it