I've seen a number of pictures of beautiful European cathedrals today, including Paris' Notre Dame and Florence's Duomo. I was wondering who would realistically have had access to them in the era in which they were constructed. Could you find a fairly representative sample of the city there? Would it be restricted just to the nobles/elite? Were regular services different from major holidays? Could children of the poor be baptized in these buildings?
1: Technically speaking, what makes a cathedral is the presence of a cathedra, or Bishop's throne. The Cathedral is the parish church where the bishop is the pastor. There's no requirement for size or grandness or architectural style. This is a Cathedral http://www.dioceseofmonterey.org/monterey-cathedral-of-san-carlos-borromeo.aspx
This is just a parish church (and always has been): http://www.bilderbuch-muenster.de/bilder/m%C3%BCnster_centrum_%C3%9Cberwasserkirche_21e4324270_978x1304xin.jpeg
2: Cathedrals have parishes just like any other church. Cathedrals tend to be located in the nicer parts of town (but they aren't always), so you can say that the congregation of a cathedral is probably going to be a little more well off than the parishes that surround it. It was common for people to attend church outside their parish if there was a famous preacher coming (this appears to have been one of the primary forms of entertainment in Late Medieval and Early Modern Europe).
3: Before the Reformation, many sacraments that were available to laypeople were not performed in the Church building, or were performed in auxilliary parts of the Church:
People were married "at the church door", rather than in the Church.
Babies were baptized either in a separate church building, or at a font located near the entrance to the church. (This is why there's a separate building for baptizing babies connected to the Cathedral in Florence, where the famous bronze doors are)
Communion was only given to the Parish in one kind (i.e. the bread but not the wine). This was done during mass, but only on special feast days.
Where it was practiced, confirmation was done in the church building, but it was far from universal.
Last rights were (and still are) brought to the place where the dying person was.
Of the sacraments that were performed in and around the Church, they would be available to all Parishioners, and sometimes people from outside the parish who were wealthy/powerful or knew somebody connected with the Cathedral.
(for more on these and other pre-Reformation rituals, and the way they transformed during the Reformation see Karant-Nunn The Reformation of Ritual [Routledge 1997])
4: Some interesting things about late medieval and early modern church arrangements: there were no pews (some people did bring their own stools to sit on) and the congregation tended to face towards the oratory (usually on a long wall of the Church) rather than the altar. This woodcut of Savonarola preaching should give you some idea of what congregations looked like. https://www.library.uq.edu.au/fryer/found_in_fryer/images/savonarola/savonarola_preaching_800s.png