Bilal, tell me: I correctly understand that with firmware correctly shooting with minimal ISO?
ISO 100 is the minimal on 650D/700D and probably the native ISO. You can already shoot at it.
I always lack light and I for the video include ISO 200 because of the fear that there will be a lot of color noise if there is ISO higher.
Add more light or use a video denoiser in post. Neat Video does a great job, also Davinci Resolve. If there is no much movement on your scene you will want to use temporal denoising.
However, MLVApp has a feature to remove color noise and then with 400 ISO footage looks not so bad. Although the same scene varies between 200 and 400 ISO...are they a little different in their sharpness...
https://mega.nz/folder/a1ojlbwK#ZFBsusu_4owrUakcbfvXUw
Higher noise = lower sharpness/details
In 650D/700D usable ISO range is 100-1600, I mean by "usable" that when switching to higher ISO . . the shadows become cleaner in cost of dynamic range (in highlights).
e.g. Going from 100 ISO to 200 ISO you get 0.9 stops cleaner in shadows, but you lose 1 stop in highlights (if there is clipping), other ISOs (this applies to video mode, in photo mode shadows might be better):
-Going from 100 ISO to 200 (+0.9 stop cleaner in shadows, -1 stop in highlights)
-Going from 200 ISO to 400 (+0.8 stop cleaner in shadows, -2 stops in highlights)
-Going from 400 ISO to 800 (+0.3 stop cleaner in shadows, -3 stops in highlights)
-Going from 800 ISO to 1600 (+0.3 stop cleaner in shadows, -4 stops in highlights)
-Going from 1600 ISO to 3200 (+0.1 stop cleaner in shadows, -5 stops in highlights)
So:
-Going from 100 ISO to 400 (+1.7 stop cleaner in shadows, -2 stops in highlights)
-Going from 100 ISO to 800 (+2.0 stop cleaner in shadows, -3 stops in highlights)
So using higher ISO in low light and as long as there is
no highlights clipping (because of higher ISO) you should use higest usable ISO from 100 to 1600.
If we matched exposure in MLVApp for your clips:
-M31-1541, 200 ISO, pushed +1 stop in MLVApp:

-M31-1540, 400 ISO:

400 ISO clip is apparently
cleaner (view images in full size), and you didn't lose highlights (you didn't reach clipping point).
Same frames
+3 stops:
-M31-1541, 200 ISO:

-M31-1540, 400 ISO:

-M31-1540, 400 ISO, with neat video:

Results will be better if you used dark-frame too (e.g. before de-noising).