As defined by the Creative Commons:
NonCommercial means not primarily intended for or directed towards commercial advantage or monetary compensation.
The "intent" here is the developer's intention, not the player's. It does not matter if a particular player - or even the vast majority of your players - intend to play your game for free. What matters is if you intend to use your game to generate revenue.
I would argue that the Freemium business model does not mean the game is NonCommercial, and that in most cases the primary intention/direction is still commercial advantage or monetary compensation.
The reason we regard Freemium as a "business model" and not as some kind of charity offer is that we recognize that non-paying players are not incidental to the revenue of a game, but in fact a key part of attracting, converting, and retaining paying players, or getting more views of paid ads.
By allowing the game to be played for free, we lower the bar for acquiring players, benefit from viral marketing by these players, keep our servers/leaderboards active & populated with partners/rivals/audiences for our paying players to interact with, and increase the "social stickiness" that keeps players coming back.
All of these factors help improve our expected revenue from the game, so the free aspect frequently supports, rather than opposes, a profit motive.
By including CC-NC music in your game, it's reasonable to suppose you're hoping to improve the player experience and perceived quality of the game, resulting in more acquisition & retention of players and better conversion rates to paying players. ie. Even though you're not selling the licensed content itself, you intend that the inclusion of this licensed content in your product will produce monetary compensation.
That would, by my reading, violate the terms of a CC-NC licence.
I am not a lawyer and this is not legal advice. You may well find others who interpret the relationship of NonCommercial use to Freemium apps differently.
But that is itself a problem.
If the interpretation is unclear, the creators of the CC-NC content you've used could interpret that your use of their creations goes outside the scope of the licence they've granted you, and take legal action against you.
You could then be put in the position of having to defend your interpretation of NonCommercial-vs-Freemium in court, at substantial cost of time and resources even if your position is correct. Very likely, this is not a possibility you want to face.
So, how can we avoid this?
Contact the creators/licensors of the content you want to use, and ask for a licence to use the content in your case.
A Creative Commons licence does not bar licensors from also offering the content under other licence conditions, so CC-NC might not be your only option.
If the licensors agree that your use is within their intention for sharing the content, then they should have no problem granting you a licence specific to your case without the interpretation risks. (Make sure you get this in writing, so you're protected in case of a misunderstanding or change of heart)
If they don't agree, then you may be able to negotiate other licence terms. As long as you both agree to a common set of terms, there should be no risk of legal fallout.
Consult a lawyer with expertise in these matters / in the relevant legal jurisdiction. They'll be able to tell you more authoritatively than we Internet randos can whether you're on solid footing or if you might be risking a (losing) battle in court.
When in doubt - if you can't get agreement from the licensors nor reassurance from a lawyer - err on the side of caution:
Use content that explicitly permits commercial use
Pay creators to license their works for use in your game
Or, do not include a paid/ad-supported aspect to your game at all (making it "Free" as in beer, not "Freemium"/"F2P"), so it cannot be interpreted as commercial
(If this is not a step you're willing to take, then it's a pretty clear sign that your intention is commercial - nothing wrong with that, it's just good to know where you stand so you can choose licensed content accordingly)
