This is an area that we need much more research on, but the evidence so far suggests a few things:
First, in some people who both consume substances and menstruate, substance use and misuse may be higher perimenstrually (around the time of the period/bleed) and possibly also around ovulation; however, findings across studies tend to be mixed, and this is likely because studies vary a lot in who they include and the methods they use.
We also know that many of the symptoms people with PMDD experience (intense, hard-to-regulate emotions, for example) are general risk factors for substance use problems. It seems likely given what we know so far that at least for some individuals, sensitivities to hormone changes across the menstrual cycle may either worsen difficulties with addiction or determine when they are at higher risk for increased use and/or relapse, but we need much more information (and the good news is that there are researchers running studies that will help inform this right now!).
All of the above points to the importance for people with PMDD or PME of developing helpful coping skills for managing cycle-induced difficult emotions as an alternative to using alcohol or drugs in problematic ways (or any other responses that cause problems). CBT and/or DBT therapy can be useful for this.
Additional reading: