I'm trying to measure relativistic speeds with an FPGA — are my results legit?
You're measuring how long

The source current of your output pin

takes to charge up

The capacitance of your input pin

through

The inductance of your coil of wire

until it reaches

The threshold voltage of your input pin.

Number 3 is related to the length of your wire, but not as directly as you would think. It's also influenced by the geometry of the wire (the value you get with it laid in a coil like that is very different from the value you would get if it made a single 100m-diameter circle) and by the presence of any conductive objects nearby. Numbers 1, 2, and 4 have nothing to do with the wire you're testing; mostly they're fixed properties of the FPGA chip, but they are liable to vary several percent depending on things like your supply voltage and the ambient temperature.
Your experiment isn't impossible, but there are several things you would have to change before you stand any chance of measuring the thing you're trying to measure. Replacing the wire with coax (to reduce interaction with the outside world) and impedance-matching the whole system would be a first step.
You may also be interested in looking up time-domain reflectometry (in which only one end of the cable is connected to the measurement device, and the length can be found by looking for the reflection of the signal from the far end) and frequency-domain reflectometry (in which, instead of sending a single pulse down the cable, we send various frequencies of sine waves, and measure the magnitude and phase of the reflected signals relative to the original). The cost of that last one has come down quite a bit in recent years.