This PARLY 2 trademark debuted in 2007. The slogan along the bottom translates directly to "the west coast spirit." Being as how the mall, Paris -nor any of its suburbs- are anywhere near a sea shore, one must conclude that something is lost in the translation. Suffice to say, the literal meaning would be more along the lines of "spirit of the west side (of Paris)."
Graphic from www.parly2.com 

This logo was introduced in 2010. The mall's location, in the Le Chesnay ["Luh shuh-nay"] commune, is mentioned at the bottom of the image. In France, a "commune" is similar to an incorporated city in the United States.
Graphic from www.parly2.com