Kind of - "trumpet" is "trompeta". On the other hand, "trompa" can translate to "horn", which is not quite the same thing as a trumpet.
In French "trompette" (trumpet) is a diminutive form of "trompe" (trunk, but it also has other meanings: [0] and trompe d'Eustache, trompe de Fallope (Eustachian and Fallopian tubes)...).