Throughout its short-lived life, the Republic of Texas attempted to build a network of roads because a) Texas has no major rivers that connect to each other without the help of canals, and b) the Republic of Texas had no money to build canals or even to entice railroads to lay tracks in their nation. So roads it was!
But the Republic didn't have much money for roads, either. Bits and sections of the network were built between 1836 and 1844. The one that came to the Red River was the Central National Road that connected Texas to Arkansas. It linked Dallas (which linked to Preston in Grayson County and Austin) to Fort Towson, Indian Territory, which then went to Washington, Arkansas.
Portions of the new highway were surveyed, marked, and tended by a commission of five men, who received land grants instead of pay.
In 1846, an ad in the New Orleans Times-Picayune tried to entice people to come to the terminus of the National Road at Pine Bluff (Red River County, Texas) where its steamship port would make it become a rival to Memphis. Pine Bluff is now... not there. It never became much of a settlement.
The map of the Central National Road was made by Betty Jo Blair for an article for the Southwestern Historical Quarterly in 1944. This carefully drawn map shows the layout of the road, superimposed on current references. This map has two sections - the broad one (shown here) and one that focuses on the road as it winds through Dallas.
Click here see the whole map, courtesy of Hardin Simmons University Library.