Yeah, a EVGA GTX 1070 FTW (not DT model) will cost about $460 USD. If you sold your FX 6300 used on Ebay, you'd have another $60- $80 to spend. this means after buying your 1070, you'd have an additional $120-$140 to play with. That's enough money for an i3-6100 but not the accompanying motherboard or DDR4 memory. It's your money: If you want to pair the GTX 1070 FTW with the FX 6300, then proceed. But the much better investment would either pairing your FX 6300 (overclocked) with a GTX 1060 or upgrading to the Intel platform with a GTX 1060.
Right now I'm playing Overwatch on a 1920 x 1200 display epic settings, MSAA 8x and get 100 FPS. BF1 I don't yet own. Fallout 4 I do own. I just tried to run it, so I can tell you that FPS that I get. It's suspiciously at 60 FPS, which makes me think that vsync is enabled, but I can't find the option. It might be in the ini file. But regardless, on my resolution I have all settings maxed out with AF at 16X. But I will mention that Fallout 4 is very CPU dependent; it's an outlier. Even a i5-6600k will bottleneck a GTX 970. i7 CPU is ideal for that title.
If I were you, I'd buy: i5-6500 (or i5-6600k) / Z170 motherboard / 16 GB DDR4 / GTX 1060 6 GB
If you can wait another 45 days or so, then you could buy the new Kaby Lake i5 CPU and Z270 motherboard.