Collosal difference between FPS in Dark Souls II and Dark Souls III [duplicate]

Since you're on a laptop, it is very possible that you are using the integrated gpu, rather than the much more powerful dedicated nvidia gpu.
You can change it in the nvidia control panel in the "Manage 3D settings" menu like this:

(Make sure you pick Dark Souls 3 in the drop-down list, or if it's not there - add the .exe manually by using the Add button.)

The system requirements for Dark Souls 2:

• OS: Windows XP SP3, Windows Vista SP2, Windows 7 SP1, Windows 8.
• Processor: AMD Phenom II X2 555 3.2Ghz or Intel Pentium Core 2 Duo E8500 3.17Ghz.

• Memory: 2 GB RAM.

• Graphics: NVIDIA GeForce 9600GT, ATI Radeon HD 5870. Hard Drive: 8 GB available space.

And for Dark Souls 3:

• OS: Windows 7 SP1 64bit, Windows 8.1 64bit Windows 10 64bit
• Processor: AMD® A8 3870 3,6 Ghz or Intel® Core ™ i3 2100 3.1Ghz
• Memory: 8 GB RAM
• Graphics: NVIDIA® GeForce GTX 465 / ATI Radeon TM HD 6870
• DirectX: Version 11

Note that these are minimum. The recommended are higher.

Your video card meets the minimum requirements for Dark Souls 2. It doesn't for Dark Souls 3.

It's worth noting that the Nvidia 9600 GT is not near as powerful as the Radeon 5870 (The two "minimum" video cards for Dark Souls 2), so the game is probably better optimized for Nvidia cards.