It will depend on how much of your old FPS was due to the FX-4300 vs. your GTX 950, & what the resolution was.
To see which is struggling more, check to see the CPU & GPU usage while playing. You can use MSI Afterburner to check your GPU usage (works with all GPUs, AMD & nVidia), & AMD's Overdrive application will let you see how much your CPU is being used. A high GPU usage with a low CPU usage would mean that the GTX 950 is struggling to display the game, which means a Ryzen CPU (or even an Intel Skylake/Kaby Lake CPU) wouldn't help; aside from turning the resolution down, the only way to fix that is with a new GPU. On the other hand, a high CPU usage & a low GPU usage would mean that your FX-4300 is holding your performance back, so you would see some improvement with a Ryzen CPU.
That being said, on this site (http://www.tweaktown.com/articles/8189/playerunknowns-battlegrounds-benchmarked-cpu-gpu-war/index5.html) they're showing both a Ryzen 5 1600X & an Intel i5-7600K hitting 66FPS on Medium @ 1080p with a GTX 1060. The problem is that the GTX 1060 is more powerful than your GTX 950; I know PUBG is supposed to be a more CPU-bound game, but the GTX 1060 (& the RX 580 they also tested with) are king of the 1080p battleground, & usually can be expected to turn in 60+FPS performances on Ultra settings; the fact that they can't on this game says something about the coding of the game (specifically, that it probably has some optimization issues that haven't been ironed out yet).
Unfortunately, I'm having trouble finding any full review sites that actually provide full benchmarks for the game -- kind of like how Techspot & Tom's Hardware do -- instead of the usual YouTuber crapshoots, so it's hard to really pick what kind of upgrade is going to help you the most. But the least time- and cash-intensive one would be to first go for a GPU upgrade. Depending on your budget, you could probably pick up a GTX 1060, or maybe even a GTX 1070, for the cost of switching over to a Ryzen build.