This is not the verb “sentir” (To feel, to smell) but “servir” (to serve, to use)

Se servir means to use, so the French sentence translates to:

Now the whole world was using the same language and the same words.

Using parler would have required to change the end of the sentence as while parler un langage is fine, parler des mots is odd.

Using avoir could have work:

Tout le monde avait la même langue et les mêmes mots