Remember, Brazoria County and Galveston County along the coast in SE Texas continue to elect a candidate in Ron Paul, who really should be a member of the Libertarian party. That area is actually very ancestrally Democrat.
Ron Paul was originally elected from a district that was suburban Houston (he defeated Mike Andrews in one election), and is now held by Tom DeLay.
His 1990s district was designed for a Democrat who switched parties and then was beaten by Paul in the Republican primary. The Galveston part of the district was added in 2003, and the portion of Brazoria county was increased.
East Texas is about the only part of Texas I would really call populist and along the border too. Rural Hispanics in Texas (and there are a lot of them), tend to be extremely populist in nature, urban Hispanics less so.
And as to your Assumption Parish question, I really have no idea. My guess, and this is a wild one, is that part of Louisiana is very much controlled by oil and gas companies. They certainly influenced Billy Tauzin while he was in Congress. I don't know how strong they were then in 1936, but it's possible they could have influenced the vote greatly in 1936, if they were anti-Roosevelt, because Assumption Parish is very lightly populated.