Seeing that you're in Shanghai, I'm surprised that it wasn't translated into "Four Seasons Royal Pavilion" - that is what 御亭 directly translates to. To answer your question, it's not uncommon to mix languages when we play the naming games. However, the capitalization you showed in that name is... rather confusing.

You may be right Parc Four Seasons could be intended to be some sort of English-French hybrid, using "four seasons" as a sort of adjective. Basically such developments can likely call themselves whatever they want, including non-grammatical phrases. The variants given seem ok. One could consider "all seasons" in English as well, as maybe more common than "four seasons", hence All Seasons Garden, Four Seasons Garden, Garden of All Seasons, ... English certainly adopts French words frequently & French also adopts English more than the French desire. A French-English hybrid is not out of the question, if in a place where readers could be expected to know some French.

I think the small 's' can make the NAME cute.

Surely it would be a 'Four Season's Park'. It needed to put an s on the end of season because its a plural, but the seasons don't belong to the park :)

Garden in Four Seasons don‘t formal ：）