The definition of the exact boundaries of the ceded territory was purposely left very loose by Napoleon.

On the east, the Spanish Government of the Floridas still kept possession of what are now several parishes in the State of Louisiana.
In the far west the boundary lines which divided upper Louisiana from the possessions of Britain on the north and of Spain on the south led through a wilderness where no white man had ever trod, and they were of course unmapped, and only vaguely guessed at.
Blindness of the American Statesmen.
There was one singular feature of this bargain, which showed, as nothing else could have shown, how little American diplomacy had to do with obtaining Louisiana, and how impossible it was for any European power, even the greatest, to hold the territory in the face of the steady westward growth of the American people.

Napoleon forced Livingston and Monroe to become the reluctant purchasers not merely of New Orleans, but of all the immense territory which stretched vaguely northwestward to the Pacific.

Jefferson at moments felt a desire to get all this western territory; but he was too timid and too vacillating to insist strenuously upon anything which he feared Napoleon would not grant.
Madison felt a strong disinclination to see the national domain extend west of the Mississippi; and he so instructed Monroe and Livingston.

In their turn the American envoys, with solemn fatuity, believed it might impress Napoleon favorably if they made much show of moderation, and they spent no small part of their time in explaining that they only wished a little bit of Louisiana, including New Orleans and the east bank of the lower Mississippi.