You mentioned that the American Civil War and French interventions almost lead to war...I presume you mean that, if Texas had gone to war against the US in 1861-1864, she would have allied with the CSA?
Another great question.
When the American Civil War starts, thousands of sympathetic Texans cross the border to join up with the CSA. Most of those Texans were southern by birth and had extended families in places like Alabama, Mississippi, Tennessee, Kentucky and Virginia. Several of those expatriates are Texas Army officers who resign their commissions to go east. Enlisted men desert in droves between 1861 and 1863.
This is a diplomatic nightmare for Texas, because those men are fighting as Texans for the Confederacy. The US protests that and other, more neutral activities such as the sale of Texas beef cattle to the CSA (even though Texas is selling to both sides.) After the US Navy blockades CSA ports, which also includes the Sabine River, Texas ships are often stopped and searched. There are a few times when Texas Navy ships are mistaken for Confederate raiders and fired upon. Smuggling across the Sabine River becomes a way of life until the fall of Vicksburg, when the US effectively controls navigation on the Mississippi.
Other Texans, however, are sympathetic to the US, and enlist as a US Cavalry Regiment in the Trans-Mississippi Department (this is actual history that I've adapted here.) Texas leverages their incorporation as US volunteers to cool the issue over expatriates fighting for the CSA. However, Kansas Jayhawkers that the US cannot control are raiding into North Texas by 1863, and only when Texas threatens to cut off sales of beef cattle does the US decide to do anything about it.
The French Intervention in Mexico (1862-1866) causes little trouble at first because it has the support of the British. But as the French established a monarchy in Mexico, Texas officially protests and refuses navigation on the Rio Grande to French troops. This brings Texas and France to the brink of war but by 1865 the French had more problems with Mexican guerillas and let the matter drop. The Texas Navy will maintain a constant presence off Brazos Santiago between 1862 and 1866. Again, shots are exchanged every now and then to make a point on both sides.
Texas will avoid war at all costs between 1861 and 1866 because of problems with hostile Indians on her frontier. 90% of her army is deployed in an attempt to contain their raids and attacks on settlements, but with marginal success. If you read about this period in Texas history, you'll learn that the frontier was pushed
back 100 miles because there weren't enough troops to cover the ground.
Those are my short answers to some very good questions.