From the wiki..
Paramore has expressed appreciation for Blink-182, Jimmy Eat World, Chicago, Sunny Day Real Estate,[54] Death Cab for Cutie, Fall Out Boy and Failure; Williams citing her personal influences as Robert Smith of The Cure and Etta James.[55] Williams explained that bands such as U2, "who are massive, and do whatever they want, write whatever they want and they stand for something", Jimmy Eat World, "who I don’t think ever disappoint their fans," and No Doubt, who "have done amazing things," act as a pattern for the path in which Paramore would like to take their career.
Can only say.. not impressed with it but she's 20 so I know when I was 20 I liked a lot of crap.. like.. oh no wait.. when I was 20 I was already a bit of a music snob.