From http://underthenews.blogspot.com ...

Perhaps you have wondered, like me, why New Orleans' newspaper is the Times-Picayune ... especially since the word picayune means "of little importance or value." Or maybe you haven't.

But, frankly, if I worked for a newspaper whose flag declared boldly it had little importance or value, I'd want to investigate further. So I went in search of an answer, and here's what I found, courtesy of word-maven Michael Quinion:

"An odd name for a newspaper, you may feel. But when its precursor, the New Orleans Picayune, began life on 25 January 1837, the main sense of the word was that of a small coin. It was at first applied in Florida and Louisiana to the Spanish half-real, worth just over six cents; in the early nineteenth century it was transferred to the US five-cent piece. The proprietors of the new newspaper gave it that name because that’s what a copy cost.

"The Beeville Bee-Picayune in Texas took its name from the New Orleans newspaper more than a century ago as a sort of homage. Could this be true also of other journals that include the word in their titles? The town of Picayune, Mississippi, was given its name by Eliza Jane Poitevent Nicholson, the owner and publisher of the New Orleans Daily Picayune, who grew up in nearby Pearlington.

"Scholars are less than totally certain about where the word came from, though the immediate origin is the French picaillon for an old copper coin of Savoy (in modern French, picaillons is a slangy term for money). In turn that derived from Provençal picaioun. Here the trail peters out, but that might have been taken from Italian piccolo, little or small, or more probably from Provençal piquar, to clink or sound."