Commies would experience serious soul-searching. Their program didn't offer a lot of alternatives, they were feeding off many ills of Yeltsin's regime, saying "This and that is bad". But they were seriously short in "what would we do differently" department. Although some doomsdayish scenario is not absolutely impossible, I don't believe this pack of greying Commie apparatchiks would do something radically serious, something like turning Russia into North Korea. They likely would start with political processes against oligarchs, masked as "tax courts" or something of this nature (OTL Khodorkovsky affair, repeated ten times), most likely returning most lucrative pieces of privatized property (oil, gas, resource industry in general) under state control. They are unlikely to go into short-term bonds the way Yeltsin's government did, therefore 1998 crisis would likely be avoided. All in all, I would look at Belarus for clues as to where this "post-Communist Russia rulled by CPRF" would go economically. State ownership of major industrial assets, combined with significant and slowly increasing private sector in retail and services.
It is hard to say what would President Zyuganov's regime do as far as foreign policy is concerned. One thing I'm very sure about is more pro-Serbian policy. Off the top of my head I can count exactly 2 cases when Russian public opinion was united across the political spectrum, one being belief that Serbs are unfairly singled out and demonized by Western political games during Balkan war and another being strong distaste of Baltic glorification of Nazi collaboration and turning Russophones there into second-class residents. OTL Yeltsin's quiet mumbling of disapprove of NATO operations in support of Albanian and Croatian ethnic cleansers was caused by his regime being dependent on Western credits, not his feeling that joint NATO-KLA operation was "peacekeeping".