It's hard to figure out where to start tackling this, and I think we need to take a few steps back in time, and also clarify that I'm going to talk specifically about England here and note that I do not know if these demographic trends existed in exactly the same way in continental Europe, though my sources indicate a certain degree of correlation. That high rate that you mention as dating to before the Industrial Revolution is actually something that happened over the course of the eighteenth and early nineteenth century (and therefore during the beginning of the Revolution) - it's not some kind of generic pre-industrial birth rate. This is attributed to a few factors:
More couples got married; fewer women lived their entire lives as spinsters. About 15% of women never married before the eighteenth century, and by the end of it, only 7.5% never married.
More illegitimate children were born. Illegitimate children rose from about 2% of births to about 6% over the course of the century.
General improvements in health outside of industrializing areas and cities led to a decrease in the amount of stillbirths, which obviously led to more children; both general improvements and the declining number of stillbirths led to fewer deaths in childbed (from about 1.3% around 1700 to about .5% in the early nineteenth century), which gave women the ability to have more children.
Women married at an earlier age, lengthening their window for having children. Over the course of this period, women's average age at first marriage dropped from 26 to 23 (and men's from 27 to 25) - more and more people were marrying in their early twenties, or even late teens.
So, okay, the high birth rate in the late eighteenth and early nineteenth centuries was a result of demographic trends specific to that time. What happened after that?
Some of the trends reversed themselves. The number of women getting married in their late teens decreased sharply from 1800 to 1880, and the number of women getting married in their twenties slightly rose. (Men had not really been getting married in their late teens, but even fewer of them did so by 1880, and other rates held fairly steady.) The main change occurred in farming couples, which had been strongly represented in the very young marriages in the eighteenth century and would go on to marry much later in the nineteenth, but other groups also reflected the trend.
While recently-married women in the nineteenth century seem to have become more fertile - they were still benefiting from better health and nutrition mentioned above - following the 1834 Poor Law, which basically made it much more difficult and degrading to be poor in England, birth rates dropped as they got older, indicating that they were most likely deliberately limiting the number of children they had. The basic pattern seems to have been that many (though not all) women would first increase the amount of time between their pregnancies, and then simply stop having babies in their late thirties or forties. (This change is also particularly evident in farming families.) So to go back to your initial premise, yes, there was "widespread contraception", if you define contraception in a broad way as simply "family limitation" or "fertility control".
No, the commercial methods of contraception popularized in the birth control movement of the early twentieth century - diaphragms and spermicide - were not available to these families. However, there were still options. The most basic were, of course, abstinence and withdrawal. These required a certain level of concentration and self-control that's irrelevant to most in the west today, but in the absence of condoms at the corner store, most had to resort to them. Abortions were also an option. Until late in the nineteenth century, a pregnancy was not generally considered "alive" until the quickening, the first movements of the fetus in the womb, and so ending a pregnancy before this point was not seen as very important (except inasmuch as this knowledge could entice unmarried women into illicit premarital sex). Medicines to fix "menstrual irregularities" or "blockages" could be purchased from advertisements in the newspaper, or folk remedies could be made - pennyroyal, steel shavings, tansy, lead - some of which could be useless and/or have serious side effects. There were also non-chemical folk remedies, like vigorous walking or riding, or taking hot baths. It was less common for women to get doctors (or "doctors") with physical instruments involved, due to the cost and, eventually, legal issues.
So, while the lowered fertility rate during the latter half of the Industrial Revolution does come down in part to family planning, I hope I've demonstrated the wider context of the demographic trends in play.
(Data mostly sourced from English Population History From Family Reconstitution, 1580-1837 (Cambridge University Press, 1997) and Barry Reay's "Before the Transition: Fertility in English villages, 1800–1880" (Continuity and Change, vol. 9, issue 1, 1994).)