Yes, scholars have referred to late medieval and especially early modern cities in western Europe as "population sinks": they could not resupply their population through fertility alone. Urban growth--and cities like Paris and especially London saw an impressive amount, even in the face of stagnating or barely increasing overall population--depended on immigration.

Modern Americans are probably most familiar with shrinking cities caused by people moving away (especially white flight). In pre-1800 Europe, however, it's clear that the biggest problem was mortality of people living in the city. Our picture of medieval cities is that they were dirty because of, well, dirt--and they were, including air pollution and dust from coal burning.

But they were also, of course, extra dirty in terms of germs. This had particularly dark implications for city populations in two cases in particular: epidemics and child mortality.

There were obviously plenty of endemic diseases circulating in cities, but flare-ups of an individual disease (plague through the seventeenth century, to be succeeded by smallpox) hit cities both harder and more often than the countryside. More people in closer proximity is obvious; cities also had people moving temporarily in and out of them from other places on a constant basis. Jeremy Boulton's studies of the London population(s) in the 16th-18th centuries showed higher mortality from plague in outlying parishes along rivers that fed into London than ones that might be geographically closer but economically/humanly more isolated.

Child mortality was exceptionally high in cities, and it actually rose over the late Middle Ages and early modern era. Infant mortality alone (within the first year of life) rose from 200/1000 to 300/1000 in some parishes. This was probably exacerbated by the inward demographic flow. Boulton observes that infant, as opposed to toddler and child, mortality was higher in parishes where immigrants tended to settle first, and suggests that women whose immune systems were not used to the city environment didn't transfer antibodies during breastfeeding. (Child mortality was higher in parishes along the rivers in and out of London, as one might expect).

Another possible factor, though nowhere near as prominent as the mortality rate, was fertility. Records seem to suggest that anywhere from 10 to 25 percent of adult women city residents were singlewomen, that is, never-married. The percentage would have been slightly smaller for men (which is harder to trace in the sources), since women immigrated to cities at a higher rate than men. Now, unmarried is not the same thing as not a mother, to be sure! Even allowing for that, there would still be a sizeable amount of the adult population who is not reproducing.

So if cities were death traps, why immigrate? In the Middle Ages, certainly, we find cases of serfs claiming the "year and a day" of residence in London to make themselves free. With respect to immigration for economic reasons, however, there are still a few groups to consider. One is international immigration, believe it or not. This was especially important in 16th century London. On the other hand, the vast majority of Paris' population growth came from the Ile-de-France and parts just beyond it (resulting in a complete stagnation or even depression in that area's population).

I mentioned women earlier, who'd often come to cities in adolescence for what we call "life-cycle" work as servants, earning a dowry for marriage or money to set up an independent household. For boys, the situation was a little more complicated. Younger boys might also move to cities for life-cycle work as servants; teenagers were more likely to have secured a place as an apprentice.

So cities were dangerous, especially for families or people who wanted to start one. But late medieval and early modern people believed it was worth the risk to immigrate.

Further Reading: Boulton's article is online for free, if you like pretty charts. ;)