Unless you stay low level as in no fire balls and remove cantrips I am not sure you can call it low magic if you do have spell caster classes. (everyone seems to have their own idea of what "low magic is" )
It depends on if your definition of low-magic is:
1. Magic is low-power AND/OR
2. Magic is fairly rare
We can rank both aspects (Power, Frequency) on a scale of 0- 3: 0 = None, 1 = Low, 2 = Medium, 3 = High.
When I say low-magic, I mean Medium (2) Power (Teleport and Raise Dead would be there, but not until 15+ level) and Low (1) Frequency.
Yes, we play low magic and I don't feel the need to restrict* classes really at all. We hold to the belief that the PCs are special. So right now our 15th level wizard is the most powerful magic user in the whole world. Next most powerful is s 12th level cleric and then most magic users (and classes in general) top out in the 5th-8th lvl range and those are "elites" with most not getting past 3rd.
*I don't restrict classes, but some spells are off the table.
I restrict classes because I think there are too many full casters. We have 4 martials, 2 half-casters (3 if you include Artificer--which I don't

), and
6 full casters!!! By removing Sorcerer and Warlock, I am restoring the balance to the class selection. Frankly, metamagic should not be a class thing, if even in the game at all (I like it better as feats so it is truly rare) and Warlock works well (in concept) as a subclass of Cleric.
Restricting the game to 6th level spells (and consequently slowing down spell progression) is a good measure as well to help create a low-magic feel.
PCs aren't inherently "special" in my games. They are special because of the things they
DO, not because of who they are. I keep some NPCs as leveled-humanoids instead of creatures like 5E does. In general, the chance of progressing to the next level is about 1 in 3. So, the chance of getting above tier 1 is less than 5%.
I think different people have different interpretations of low-magic. I would definitely not consider a party of a paladin, ranger, cleric and wizard as low magic!
For me, in a low magic campaign you would have maximum 1 half or full caster.
Rangers and Paladins would be non-casters OR have there spell progression more like 1E (not until tier 2 to tier 3).
With making spells selected by slot as they were in AD&D as well, even having two full casters would feel less magical. Having the ability to cast a prepared spell with any available slot makes magic to adaptable and open. So, that is another issue.
Finally, low-magic is also a lot about the world the PCs are in, as well as what the party itself can do.