I've been reading about this!
During menstruation, a woman’s serotonin levels are at their lowest. And because carbohydrates (via insulin) increase the availability of the premier amino acid precursor to serotonin (tryptophan), craving carbs during your period is totally natural. It probably just means that you are low in serotonin (which, according to the research, you likely are) and your body wants to make more of it.
As for whether or not this is problematic, sports science offers another clue: during the mid-luteal phase (the two weeks leading up to menstruation) when estrogen dominates, the potential for glycogen storage is maximized. What that means is that for two weeks before your period rolls around, your muscles are primed to accept and store carbohydrate as energy (rather than as fat). I wouldn’t suggest you give in to the carb cravings as they typically manifest – muffins, cakes, pizza, cookies – but this might be a better time to eat a few Primal-friendly sources of carbs. Think sweet potatoes, white potatoes, yams, squash, and various types of fruit. Oh, and high-quality dark chocolate, if that’s your thing. The fact that your cravings only surface during your period tells me that you’re in a good place, nutritionally, and that these cravings are physiologically normal.
From marksdailyapple.com