There are four versions of Lakes of Ponchartrain in the DT and another above, but this one doesn't mention alligators and has other differences.

Lyr. Add: ON THE BANKS OF THE OLD PONCHARTRAIN

I traveled from Texas to low Louisian',
Through valleys, o'er mountains and plain.
Both footsore and weary, I rested a while
On the banks of the Old Ponchartrain.

The fairest young maiden that I ever saw
Passed by as it started to rain.
We both found shelter beneath the same tree
On the banks of the Old Ponchartrain.

I ventured a smile, but she thought I was bold.
I hastened to try and explain,
But somehow I knew I would linger a while
On the banks of the Old Ponchartrain.

We hid from the shower an hour or so.
She asked me how long I'd remain.
I told her I'd spend the rest of my life
On the banks of the Old Ponchartrain.

As time drifted by, we fell deeper in love,
A love that could just bring her pain.
I knew that one day I would leave her alone
On the banks of the Old Ponchartrain.

I just couldn't tell her that I ran away
From jail on an old Texas plain.
I prayed in my heart I would never be found
On the banks of the Old Ponchartrain.

Then one day a man put his hand on my arm
And said I must go west again.
I left her alone without saying goodbye,
On the banks of the Old Ponchartrain.

Tonight as I sit here alone in my cell,
I know that she's waiting in vain.
I'm hoping and praying someday to return
To the banks of the Old Ponchartrain.

Sung by Mrs. W. B. Apple, recorded 1962, learned from Lolly Linebarger. Wolf Folklore Collection (Lyon College, Batesville, AR): Ponchartrain

Another version is in the collection, titled "Creole Girl," recorded 1958. Creole Girl