Tulane is a workable option for an international business law job, but not the best one. You will need to be in the top 5% of your class, or have some other eye-popping credentials, to get your foot into the door at most serious employers.

If you have good undergrad grades and LSAT scores, consider big-name schools. NYU, Berkeley, Stanford or any place in the Ivy League will get you into this sort of job lickety-split. Yes, you'll have to go into debt, but the degree will pay for itself when you're making $145k plus bonuses in your first year out, whereas if you stay in-state, you could EASILY end up settling with a crappy $50k job at a no-name firm in Shreveport, wondering where you went wrong.

Disclaimers that should be on every law school application:

1) Your class rank in law school will probably be much worse than you expect it to be (everyone is an overachiever, even in the middle-tier schools, and you're graded on a curve).

2) The average starting salaries which most schools publish are highly inflated.

An MBA is a good choice if you're staying in-state, since it will make you more qualified for quasi-lawyering jobs like the one described above.