Our Proto-Indo-European root is *bʰreg- "to break". The zero-grade nasalized form *bʰr-n-g- became Latin frango "to break", pp. fractus "broken", giving us words like fractal, frangible, fragile.
The Oxford Dictionary of English Etymology says sassafras is from Spanish sasafrás or Portuguese sassafraz, of unknown origin. But the AHD says the Spanish is from Late Latin saxifragus "rock-breaking" (from its being found in rock crevices), a combination of frango and saxum "rock" (from PIE *sek-). The plant genus Saxifraga is so named for the same reason.
*bʰreg- became Proto-Germanic *ƀrek- and English break and breach. The Proto-Germanic form was borrowed into Old French, becoming brier "to knead", then brioche.