Hmm... I'm late to the party and I didn't read every post. Presumably the answer has been given, but I'll just add in case no one mentioned this.
The question in debate is whether or not it was scientifically accepted to say that there would be gravity at the center of the Earth at the time that Jules Verne wrote "Journey to the Centre of the Earth".
Was it a scientifically valid theory (or hypothesis) to say that there would be gravity, in the sense of being able to walk around normally, in 1864?
There is no net gravitational acceleration at the centre of an isotropic mass distribution. The proof for this is quite simple and was given by Newton in the Principia in 1687.
Note that this does notsay that there is no gravity, just that the net acceleration due to gravity is zero.
This proof needs two assumptions: there is no other source of gravity (fairly good approximation on Earth; the Earth is very clearly the dominant source of gravity near here. Tides are irrelevant to this) and the mass distribution is spherically symmetric (ie, radial shells have a uniform density). This is also a fairly good approximation. True, the Earth is neither smooth nor spherical, but the deviations are small.
So no, there was no reason to say that there was gravity at the centre of the Earth in 1864. It's been a long time since I read Journey to the centre of the Earth, but as far as I recall, Jules Verne says as much at one point and makes no claim to the contrary. Note that the journey described in the book comes no where close to the centre of the Earth anyway.
Wait, it is true that all objects with mass effect all other objects with mass gravitationally, right?
Yes. Actually, all objects that have energy (which is all of them), since gravity acts on energy rather than mass.
Proportionally to their masses and inversely proportional to the distance between them, right?
Mmmmmmmmmmsortofmostofthetimebutnotreally. See below.
Or is that under contention as well?
Not at all. Gravity in general is described by Einstein's theory of general relativity, which is not F=GMm/r2 er but something more complicated. However, in the low energy/low velocity limit, it reduces to Newtonian gravity.