Gaussian Fit on noisy and 'interesting' data set

As mentioned in the OP comments, one of the ways to constrain a signal in presence of unwanted data is to model it together with the desired signal. Of course, this approach is valid only when there is a valid model readily available for those contaminating data. For the data that you provide, one can consider a composite model that sums over the following components:

1. A linear baseline, because all your points are constantly offset from zero.
2. Two narrow Gaussian components that will model the double-peaked feature at the central part of your spectrum.
3. A narrow Gaussian component. This is the one you're actually trying to constrain.

All four components (double peak counts twice) can be fit simultaneusly once you pass a reasonable starting guess to curve_fit:

def composite_spectrum(x, # data                       a, b, # linear baseline                       a1, x01, sigma1, # 1st line                       a2, x02, sigma2, # 2nd line                       a3, x03, sigma3 ): # 3rd line    return (x*a + b + func(x, a1, x01, sigma1)                    + func(x, a2, x02, sigma2)                    + func(x, a3, x03, sigma3))guess = [1, 200, 1000, 7, 0.05, 1000, 6.85, 0.05, 400, 7, 0.6]popt, pcov = curve_fit(composite_spectrum, x2, y2, p0 = guess)plt.plot(x2, composite_spectrum(x2, *popt), 'k', label='Total fit')plt.plot(x2, func(x2, *popt[-3:])+x2*popt[0]+popt[1], c='r', label='Broad component')FWHM = round(2*np.sqrt(2*np.log(2))*popt[10],4)plt.axvspan(popt[9]-FWHM/2, popt[9]+FWHM/2, facecolor='g', alpha=0.3, label='FWHM = %s'%(FWHM))plt.legend(fontsize=10)plt.show()

In a case when the unwanted sources can not be modeled properly, the unwanted discontinuity can be masked out as suggested by Mad Physicist. For a simplest case you can even simply mask out eveything inside [6.5; 7.4] interval.