Checking Parseval's Theorem for Gaussian Signal by Using Scipy
There is a simple idea behind Parseval's Theorem.
Unitary transform preserves the $ {L}_{2} $ Norm.
The Fourier Transform (All its variants) are indeed Unitary when the correct factor is in place.

The problem is with the way you sum the elements and factor them.
What you need to factor by $ \frac{1}{N} $ is the sum of squared absolute value of the series.

Have a look on the following MATLAB Code:

numSamples = 50000;
vT = linspace(-1000, 1000, numSamples);
vH = exp(-(vT .* vT));

vK = fft(vH);

% Summation by Parseval Theorem

sum(vH .* vH)
sum(vK .* conj(vK)) / numSamples


In MATLAB it yields

ans =

   31.3322

ans =

   31.3322


Why is that?
Pay attention that the fft() applied by MATLAB and Python is not the Unitary form.
For the unitary form it should be factored by $ \frac{1}{\sqrt{N}} $.  

Yet in Parseval we see:

$$ \sum_{n = 0}^{N - 1} {x}^{2} \left[ n \right] = \frac{1}{N} \sum_{k = 0}^{N - 1} {\left| X \left[ k \right] \right|}^{2} $$

The factor $ \frac{1}{N} $ is exactly $ {\left( \frac{1}{\sqrt{N}} \right)}^{2}$.