"The more things change, the more they remain the same". How do you
say that in the original French?

The original French version of this quote is "Plus ça change, plus
c'est la même chose."

"QUOTATION:  The more things change, the more they remain the same.
            [Plus ça change, plus c?est la même chose.] 

ATTRIBUTION: Alphonse Karr (1808-1890), French journalist, novelist. 
             Les Guêpes (Paris, Jan. 31, 1849)." 

The Columbia World of Quotations
http://www.bartleby.com/66/88/32088.html

Google search strategy:

Google Web Search: "the more things change" "plus ça change plus c'est
la même chose"
://www.google.com/search?hl=en&q=%22the+more+things+change%22+%22plus+%C3%A7a+change+plus+c%27est+la+m%C3%AAme+chose%22

I hope this is precisely what you need. If anything is unclear or
incomplete, please request clarification; I'll be glad to offer
further assistance before you rate my answer.

Best regards,
pinkfreud