Hello Toufiq,
I tried to make it on your Demo page but, I do not know why, the language switcher does not appear on the home page (even if plugin is enabled). However at the mean time, I found what the problem was on my website. Only for the UK language (which is the deafult language), when I edit the SP Portfolio type of Menu Item, I can select the English-Cat Category I have created and then the tiles of SP Portfolio are showing and items too. Unfortunately if I re-edit the same SP Portfolio type Menu Item, then the previous selection of English-Cat category is gone. It means I have to re-select the Category in the SP Simple Portfolio Settings (it does not keep it in memory). It is a strange behaviour as on all other Simple Menu type menus of oher languages, once you have selected the proper category in the SP Simple Portfolio Settings, it will stay.