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Thank you for contacting WPML Support. Was your site previously set at http and then changed to https? In that case elements (like the switchers) you may have created at that time may be still showing an old value.
If you have problems with mixed content warning after update from http to https with WPML language switcher, there is the possibility that the language switcher is still being cached.
You can try and clear the cache from WPML > Support > Troubleshooting -> Clear WPML Cache and also to disable the template language switcher cache.
Another workaround would be to remove all language switchers and re-add them manually.
Please check also if you have "WP_SITEURL" or "WP_HOME" defined in your wp-config.php. If so, check if they're using https instead of http. you can also try to remove them and see if the errors persist.
Please check also if you're using any caching plugin in your site or server. Try to deactivate them and check if the issue persists.