Hello,
Thank you for the quick answer, here are the data:
1. wp_posts post_title:
polylang_mo_20, polylang_mo_22, polylang_mo_35
2. wp_taxonomy term_id:
20, 22, 35
3. wp_options _transient_pll_languages_list:
a:3:{i:0;O:12:"PLL_Language":20:{s:7:"term_id";i:20;s:4:"name";s:9:"Français";s:4:"slug";s:2:"fr";s:10:"term_group";s:1:"0";s:16:"term_taxonomy_id";i:21;s:8:"taxonomy";s:8:"language";s:11:"description";s:5:"fr_FR";s:6:"parent";s:1:"0";s:5:"count";i:148;s:10:"tl_term_id";i:21;s:19:"tl_term_taxonomy_id";i:22;s:8:"tl_count";i:18;s:6:"locale";R:9;s:6:"is_rtl";s:1:"0";s:8:"flag_url";N;s:4:"flag";N;s:8:"home_url";s:36:"http://127.0.0.1:8080/cimediapro/fr/";s:10:"search_url";s:36:"http://127.0.0.1:8080/cimediapro/fr/";s:4:"host";N;s:5:"mo_id";s:4:"1059";}i:1;O:12:"PLL_Language":20:{s:7:"term_id";i:22;s:4:"name";s:7:"English";s:4:"slug";s:2:"en";s:10:"term_group";s:1:"1";s:16:"term_taxonomy_id";i:23;s:8:"taxonomy";s:8:"language";s:11:"description";s:5:"en_US";s:6:"parent";s:1:"0";s:5:"count";i:113;s:10:"tl_term_id";i:23;s:19:"tl_term_taxonomy_id";i:24;s:8:"tl_count";i:16;s:6:"locale";R:29;s:6:"is_rtl";s:1:"0";s:8:"flag_url";N;s:4:"flag";N;s:8:"home_url";s:36:"http://127.0.0.1:8080/cimediapro/en/";s:10:"search_url";s:36:"http://127.0.0.1:8080/cimediapro/en/";s:4:"host";N;s:5:"mo_id";s:4:"1060";}i:2;O:12:"PLL_Language":20:{s:7:"term_id";i:35;s:4:"name";s:8:"Română";s:4:"slug";s:2:"ro";s:10:"term_group";s:1:"2";s:16:"term_taxonomy_id";i:36;s:8:"taxonomy";s:8:"language";s:11:"description";s:5:"ro_RO";s:6:"parent";s:1:"0";s:5:"count";i:112;s:10:"tl_term_id";i:36;s:19:"tl_term_taxonomy_id";i:37;s:8:"tl_count";i:17;s:6:"locale";R:49;s:6:"is_rtl";s:1:"0";s:8:"flag_url";N;s:4:"flag";N;s:8:"home_url";s:36:"http://127.0.0.1:8080/cimediapro/ro/";s:10:"search_url";s:36:"http://127.0.0.1:8080/cimediapro/ro/";s:4:"host";N;s:5:"mo_id";s:4:"1078";}}
In the live database, instead of http://127.0.0.1:8080/cimediapro/ is http://www.cimediapro.com.
I hope this is helpful to find where the problem is.