You're dead wrong. It specifically states it's a "right of the people". The militia is just all persons, originally all males, able to bear arms. But never mind that. What about this provision of the Louisiana Constitution?
"The right of each citizen to keep and bear arms shall not be abridged, but this provision shall not prevent the passage of laws to prohibit the carrying of weapons concealed on the person." Article 1, Section 11.
Think that the Louisiana Constitution can't be enforced against it's government?
Or if you live in Texas, as about 250,000 Louisianans now do
"Every citizen shall have the right to keep and bear arms in the lawful defense of himself or the State; but the Legislature shall have power, by law, to regulate the wearing of arms, with a view to prevent crime." Article 1, Section 23.
Or should you find yourself in Nebraska
All persons. . . have certain . . . rights, among these are . . . the right to keep and bear arms for security or defense of self, family, home, and others, and for lawful common defense, hunting, recreational use, and all other lawful purposes, and such rights shall not be denied or infringed by the state or any subdivision thereof." (Article 1, Section 1).
And lets remember that the Constitution does not grant or create this right , but only recognizes it.
This is one of those inalienable rights that men have by nature and can not be eliminated .... only violated.