That is absolutely correct. That is the real reason for the need to control the Mississippi River by the Federals. That control was really a part of the Anaconda Plan because the flow of supplies to the Confederacy through Mexico could not be practically cut off in any other manner. And while the Federal Blockade of the Mississippi River was never airtight, shipments east or west across the Mississippi were not totally stopped, but some things were severely curtailed, primarily Texas Beef.
In any case the Texas-Mexico trade and the French connection in my opinion has never been fully addressed. Most seem to concentrate on the English trade and Blockade runners.