I had the same issue I was with i5-2320 @ 3Ghz, which is old but not obsolete it handles fine most of the games as BF3 BF4. I had 12 GB DDR 1333Mhz ram, and I sold my GTX 960 2gb cuz I wanted to have more quality and performance and the same time in Battlefield 1, that I5 and 960 and 12GB ram couldn't do anything even on low settings I was on 45 fps I run my windows 10 pro on my SSD 120 GB and games on my WD Blue 1T 7200rpm's, and what I did just buy right away Asus Strix ROG GTX 1060 6GB @ 1506Mhz Default Turbo Boost 1709, with final result maximum she was getting 1886Mhz not OC. And me jumping in-game BF1 noticing that at any settings on 1080p res I am by the way, on any settings either low, med, high or ultra I get same FPS max 55 lowest 23 avg 30 or so, even when I got those 55fps the FPS drooped @ 15-20FPS suddenly.
And I was like WTF I have so strong card wtf is going on. New drivers older drivers all the same, and with my last budget, I decided to see if anything bottlenecking anything to find out and by if something is needed. On checking upon bottlenecking I found out that my i5-2320 @ 3ghz, TB 3.3ghz was doing 29% bottlenecking on the GPU. OK, I was like time to upgrade the CPU so with my current budget and the available CPUs I bought the i7-3770 @ 3.4Ghz TB @ 3.9Ghz.
And then only then I felt difference in the FPS on different settings I was getting different FPS, but I was struggling to play on Ultra preset Battlefield 1 because that CPU and GPU should handle 1080p with awesome results, but on Ultra I had issues, I had the fps more or less but I had the same issue of dropping frames, and I was like come on, what now. Ok I said to my self with the last money that I have and the Ram that I had of 12 GB and the ram that I had one was 8GBs @ 1600mhz and the other plate of 4GB was on 1333Mhz and both were running on different CL speeds, I managed to sell them both and I got 2 x8GB DDR3 RAM @ 1600Mhz and then with all this taken care of, I add the game on ultra believe or not I was averaging 80FPS on 64p servers in very intensive close corners scenes with bombs and all that the FPS dropped to 62, so the most stressful maps on BF1 with full 64p server. On other maps same with 64p I was easy on 100FPS then on 90 or 80 or 70 and back to the sweet spot of 85 most of the time the FPS was just there 85. So I don't know how but I explained my situation here and you can see if something bottlenecking any part CPU to GPU or GPU to CPU it's not good, changes must be applied Immediately.