Although the first step to living a Paleo lifestyle is to consume lots of plants, mostly we mean vegetables and some of the lower-carb fruits such as tomatoes, peppers, and cucumbers. The sweeter fruits can absolutely be included as part of a healthy Paleo lifestyle, just remember to moderate your consumption.
The Nutrient Content of Plums
Plums are fairly high in carbohydrates, and most of those carbs are straight sugar, with only a nominal amount of dietary fiber. They are a good source of vitamin C, but contain only small amounts of other nutrients, such as B vitamins, magnesium, phosphorous, and potassium. They are high in antioxidants, though, which are necessary for maintaining a healthy immune system and protecting against chronic conditions such as diabetes and heart disease.
Mark Sisson listed plums and prunes among the fruits with the most antioxidants in this post.
As far as whether the carbohydrate content of plums will have a negative or positive effect on your health goals, that is entirely individual. Some people find that they thrive on a diet that is extremely low in carbohydrates, while others find that they require a slightly higher carbohydrate content. This can depend on factors such as your activity level, but the bottom line is that self-experimentation is the only way to know what works best for you. Play around with your carbohydrate content and see what makes you feel your best.