An obvious reason for an American to learn Spanish is the large number of Spanish speakers in the country. What arguments could one make for studying French or Italian instead?
French is a world language, useful for understanding not only Europe but also swaths of Africa and some of Asia's colonial history as well. Spanish (and Portuguese) likewise open vistas onto different parts of the world. You can't really make as powerful a case for Italian in this regard.
There are different things to *enjoy* with each language. Your child might want to dip into some French or Spanish lit in translation and see if there are writers appealing enough to want to read in the original. There is some wonderful poetry in French. Italian is beautiful and fun.
Having any of these languages, it is not tough to pick up the others in any case.
