In the sense of causing trouble, these words can be used interchangeably: "Rebel soldiers fomented (or fermented) unrest among the people." Ferment literally means "to act upon as a ferment," that is, to cause the giving off of gases that induce bubbling and rising: "The mash will ferment for several days." Because fermentation is a state of unrest and agitation, as a noun ferment means "excitement," "commotion," and "tumult": "The lover's mind was a ferment of emotions." To foment is "to cause rebellion or discord," "to incite," "to arouse," "to inflame": "The inmates of the prison tried to foment a rebellion against the guards." Foment, a verb only, conveys the idea of causing unrest; ferment, both noun and verb, stresses the idea of being in, rather than causing, a state of unrest.
Dictionary of problem words and expressions. Harry Shaw. 1975.