I am inclined to think that if we accept certain physical laws as foundational beliefs that are necessarily true, then the argument for unsupported objects falling towards the Earth does seem to become more deductive in nature. The issue then is how you justify your foundational belief in gravity without relying on inductive reasoning.
Hume would say that just because we have always in the past witnessed unsupported objects falling down, it does not necessarily follow that they will in future. We assume that they will, through habit, as this is useful to going through every-day life.
Perhaps the solution is to reclassify the law of gravity from a "matter of fact" to a "relation of ideas". To some extent this is what Kant seems to do with his metaphysics. Space and time, for Kant, are not matters of fact but are a priori ideas which give the structure to our experiences.
Could the law of gravity be regarded as inherent in our idea of space? I personally think this is doubtful, but I still want to be able to say that the law of gravity is somehow "necessarily true".
Is the law of gravity falsifiable, in a Karl Popper sense? My initial response answer is "yes, obviously it is" and as such it is a scientific fact. But could we really find evidence to falsify the law? I think the answer may in fact be "no". If we were to find circumstances where objects did not obey the law of gravity we would not abandon the law but would modify it for those unique circumstances. An example I have in mind is quantum mechanics, where some quantum objects do not in fact obey the law of gravity.
So in one sense I don't think the law of gravity is falsifiable, at least in the world that we live in on a non-quantum scale. Anybody who claimed to witness an apple which didn't fall towards the Earth when they dropped it would not be taken as having found evidence against gravity, we would have to assume that they were under a misapprehension, or there were some other physical conditions preventing the apple from falling of which we were not aware. Evidence for absence of gravity must take on the nature of Hume's idea of a miracle, where the natural order is temporarily suspended. Hume rejects miracles as being, by definition, virually impossible.
In conclusion, I personally think there are some physical laws which are 'necessarily true' because they are how we make sense of the world. This is not to say that they cannot be modified or extended in certain unique circumstances, but for "regular" circumstances they must apply.
Could we then have a third form of argument which sits somewhere between induction and deduction? What would it be called?