Well, there's a short answer to your question and that goes: Yes, absolutely! But short answers are seldom really satisfactory, and so I'll try to extrapolate from what I know about Catholic churches of that time in general onto Notre-Dame, which I'm afraid I have never visited and probably won't be able to visit for a long time.

First, let's take a look at a floor plan. This plan shows Notre-Dame and its environs in the years 1750, 1550 and 1150, respectively. Do you see the many small rooms along the wall? Those are chapels; small enclosures sporting an altar and probably a small number of pews. It was a key feature of early modern Catholic churches that virtually all of them besides the smallest ones had both a main altar and a number of so-called "side altars"; St Stephen's in Vienna for example had 38 of those minor altars in 1779. The function of those smaller altars was twofold: On the one hand, the prevailing attitudes amongst medieval and early modern Catholics meant that being able to finance the construction of an altar was seen as highly beneficial for the welfare of your own soul. Contributing to the glory of the Church by creating a sacred space where the sacrament of the Eucharist could be held regularly (i.e. where by Catholic dogma God Himself descends onto Earth) was something that a whole lot of people aspired to. And secondly, it was anothe feature of early modern Catholicism that the number of "ordered Masses" was enormous. Arranging for Masses to be read in your name after your death was seen as not only a great way to keep the memory of you alive, but it was the firm belief of virtually all Catholics that through that way it was possible to shorten your soul's time in purgatory, a sort of "waystation" or "quarantine" in which your soul is cleansed and readied for Heaven. Many believed this process to be long (as in thousands of years long), arduous and very painful. Shortening your time in purgatory by ordering Masses in your name was therefore extremely frequent, and in turn ordering Masses for other people that already were dead was a great act of charity and thereby beneficial for your own soul too.

So, owing to widespread Catholic beliefs of that time, many churches not only had a great number of altars but also a corresponding number of priests that kept busy reading Masses and trying to meet the high demand. In aforementioned St Stephen's, 150-200 Masses were read every day. The minimum time one Mass was required to last was 20 minutes; so if we go with the lower number of estimated daily Masses, assume that every Mass only took those 20 minutes and that every altar saw the same number of Masses read on it per day (all of these assumptions being likely false), then even under those circumstances we would say about four Masses or a full eighty minutes of liturgy per day and altar. Notre-Dame will have been similar, so you need to envision it as a never-ending stream of Masses, beginning (like most Catholic churches) at five or six in the morning and going on until late evening, only interrupted by a short break around noon.

But the many Masses weren't the only thing taking place in an early modern Catholic church. There were devotions, the liturgy of the hour. processions in- or outside of the Church, rosaries, litanies, homilies (which back then were separate from the Mass itself) and so on. Confraternities would hold prayer meetings, altar boys would be instructed in the art of serving at Mass, people would pray the rosary or go to confession and so on. An early modern Catholic church was in all likelihood not a place for silent and prayerful devotion, but could actually be quite loud and chaotic, and that extended beyond the religious: We have numerous reports from that time written by exasperated priests about how their flock didn't seem to care a whole lot about the sanctity and sacrality of their beloved churches. Young people could regularly be found flirting especially in the darker and less visible corners of a church, merchants were striking business deals, unruly youngsters were throwing paper planes from the gallery, kids were playing hide-and-seek between the columns etc.

So, to go back to your initial scenario: If you were an average person living in Paris and you didn't belong to the (still small) number of anti-clerical Catholics that could be found in France back then, then you would probably find yourself in a church not only once every Sunday (every Catholic was and in theory still is required to attend Mass in his or her parish church on Sunday), but several times throughout the week as well. You would probably keep an eye on the announcements and schedules of the many churches and monasteries to be found in Paris: Which preacher could be heard when and where? Which services were connected with an especially powerful blessing - maybe it was a specific church's patron saint's feast day and the saint's relics were brought out for veneration? Or maybe the bishop or another high-ranking prelate would read Mass and spend his blessing afterwards? Or maybe a freshly ordained priest would be reading Mass for the first time, during which his blessing was said to be extremely powerful? Or maybe you were the member of a confraternity whose statutes promised you a powerful indulgence if you were saying a specific prayer in a specific church on a specific day... you get the idea. And if it wasn't the blessing that lured you into church, then often it was simply the spectacle - living in a larger Catholic city meant that you could hear live music, often composed specifically for today, multiple times every day in the various churches around you. Pontifical Masses were full of a splendour you simply didn't get to see every day, and the many processions weren't simply ostentatious displays of ecclesiastical presence, but could also be read by the attentive onlooker like a book detailing the current social hierarchy between the many groups and factions in the city - which religious order was allowed to go directly behind the Eucharist? Did Judge X finally complete law school, or was he still wearing the simple black robes of those judges without a diploma? Who was having the privilege of walking besides the King that day? And so on.

Most Catholic churches of that era weren't simply spaces in which a priest did whatever priests were supposed to do. They were instead both the sacred spaces and welcome meeting grounds of the entire community surrounding them, bustling with life. Your average Parisian probably didn't visit Notre-Dame every day, but there probably was hardly a man, woman or child in the city that couldn't at least occasionally be found in this ancient church.