Ha! No, that's just the local naming since Toulouse has several of them, they have proper names in addition to the numbering. Toulouse I Capitole is (mostly) law and economics, Toulouse II Jean Jaurès is (mostly) social sciences/humanities/linguistics and Toulouse III Paul Sabatier is (mostly) STEM.
My alma mater is technically Université de Toulouse, the federating entity that formally gives the diploma, but the existence of such entities depends on the city, each university has its own head and administration. My grad school lab was attached to Toulouse III.