The Emancipation Proclamation in part reads as follows:

That on the first day of January in the year of our Lord, one thousand eight hundred and sixty-three, all persons held as slaves within any State, or designated part of a State, the people whereof shall then be in rebellion against the United States shall be then, thenceforward, and forever free; and the executive government of the United States, including the military and naval authority thereof, will recognize and maintain the freedom of such persons, and will do no act or acts to repress such persons, or any of them, in any efforts they may make for their actual freedom.

That the executive will, on the first day of January aforesaid, by proclamation, designate the States, and part of States, if any, in which the people thereof respectively, shall then be in rebellion against the United States; and the fact that any State, or the people thereof shall, on that day be, in good faith represented in the Congress of the United States, by members chosen thereto, at elections wherein a majority of the qualified voters of such State shall have participated, shall, in the absence of strong countervailing testimony, be deemed conclusive evidence that such State and the people thereof, are not then in rebellion against the United States.

It is a bit of a word soup, but the key takeaway here is that the Emancipation Proclamation only applied to States, or the part of States then considered in rebellion. If it was under Union control, the Emancipation Proclamation didn't apply there. And while some like to be cynical and claim that this points to Lincoln's lack of conviction about ending slavery, and that he only was interested in it as a carrot and stick to induce the end of the rebellion or else punish those who continued, the much more simple explanation is that Lincoln didn't believe he had the Constitutional authority to do more than what he was doing.

Ending slavery in the country as a whole by Presidential fiat would have been unconstitutional, and although attempts were made during the war in the border states still loyal, it was generally unsuccessful as it required agreement of the state governments. The process for ending slavery was begun in late 1863, the the 13th Amendment being drafted and worked on by Congress through the following year and eventually sent for ratification following the House vote in early 1865. Lincoln knew that he needed to follow that process to wipe out slavery nationally. But, he felt that he could do so with his own pen in the areas where the states were in rebellion, believing that he was vested with this power under Article II, Section 2 of the Constitution naming him Commander in Chief of the armed forces.

So anyways, the point is, the Emancipation Proclamation only applied to where the Confederates controlled, because Lincoln didn't believe he had power to do more. As this applies to Louisiana specifically, by the time the Emancipation Proclamation came into effect, on January 1, 1863, by that point Louisiana was partially under Union control, New Orleans having been captured in early 1862, and due to a decent minority of pro-Unionists, it regained partial Congressional representation, with Michael Hahn and Benjamin Flanders taking seats for the tail end of the 37th Congress that December (although this would be brief, and none would be seated for the 38th Congress). So in short, at the time of the Emancipation Proclamation's implementation, a portion of Louisiana was under Union control, and had members sitting in Congress, which very clearly exempted those parts of the state from being within the purview of the Emancipation Proclamation.