Are these One Piece characters based on western children's story characters?
Usopp's name is derived from the Japanese word "Uso" which means lie or falsehood (1). The elongated nose is an allusion to Pinocchio. 

Franky was actually created with seiyu Kazuki Yao in mind after Eiichiro Oda (the mangaka) heard the voice actor's performance as Jango and Bon Clay, however it is likely that Franky is based on Pop-eye. In addition to the enlarged forearms, both characters are 34 and both rely on food for energy and powers (Popeye uses spinach and Franky uses cola) (2).

There are numerous clues that Chopper is an allusion to Rudolph (taken from this Wikia article):


Chopper is a reindeer with an odd colored nose
His official birthday is Christmas eve
"Chopper the Blue-nosed Reindeer" was produced and sung by the cast
Dr. Kureha is described coming down the mountain with Chopper's silhouette pulling a sleigh and then enters some homes via chimney