6:48 AM PT -- Officials tell TMZ Sports ... Williams was initially pulled over for going 80 in a 50 on the Crescent City Connection Bridge.
During the stop, cops suspected he was intoxicated and tried to administer a breath test but Williams refused ... so he was arrested.
We're told he was booked for driving while intoxicated, speeding, improper lane usage and failure to use a turn signal. A bad week just got worse for New Orleans Saints cornerback P.J. Williams -- who was arrested early Wednesday morning when cops say he was driving drunk in the Big Easy.