"Approximately 19 percent of the 'Defenders of the Native Land' militia enlisted in the 1st Regiment [Union Native Guards], and another 14 percent joined other Union regiments during the war."

Black Patriot and a White Priest by Stephen Ochs, page 76

I got the same result- 33% (about 300 out of 906). Of that number about 100 served in a regiment of home guards (6th LA) that served but 40 days.

It should be noted that the North had far more inducements to join the Federal army- bonus money, land, equal pay, &c.
The State of Louisiana had nothing other than an appeal to patriotism.