"private international law" (not "international private law") is the area of law that involves dealings between individuals, and includes business law. However, if you look at course discriptions for the "juriste d'affaires internationales" it is solely concerned with business rather than things like divorce and succession.

The 'juriste' bit is always tricky, but I normally prefer to translate it as "lawyer". Just because 'juristes' do not have the same rights to practice law that an 'avocat' does doesn't make them any less a lawyer. "Juristes" have a lot in common with solicitors, but solicitors have more rights to appear in court than 'juristes'. Consequently the bland 'lawyer' is the least incorrect, IMHO.

However, because this is a course name, I actually would suggest not putting it in. A course title of 'international business law specialist/lawyer' sounds odd in English, better to drop it, I think.

The DESS is bac+5 so somewhat equivalent to a Masters or perhaps a post-graduate diploma.

So perhaps the best translation would be along the lines of:

"Post-Graduate Diploma in International Business Law"

The word jurist does exist in English but is rare... If the degree is a law degree, then whether or not the person is an avocat a la cour, s/he is a lawyer or attorney.