Is it possible for my ex to forgive me and give me a second chance?

his girl is from France.

My ex broke up with me a month and a half ago, we had a mutual agreement to try and fix things between us a couple weeks after but I messed it all up with my trust issues. A month later I am on the edge of losing her all together. I made a fake profile to hammer information out of a guy I was suspecting her of being romantically interested and I got it. I was afraid to ask her about any other guys in her life because she hates me asking about them, but I wasn't sure if she would even give me a truthful answer. I made the mistake of telling her what I did, because I could not live with it. We are on a break right now and a few days before she told me she could not trust me the same ever again after the fake profile deal. I have said I would change months ago near our break up, when I was begging to be in a relationship which is one of the most unattractive things you can do after a break up. However, have noticed after our break started I feel Empowered/enlightened that I could really really change, I guess it is because you never realize what you are capable of until you are stumbling on the edge of death. I have taken the greatest change ever, i took the past few days of not being able to eat as a sign to lose weight and get in shape, and also confronting nostalgia and learning french even though it makes me sad.

She still wants to be friends, but told me that "she doesnt think she will ever have feelings of love towards me again, and as of right now she doesnt want it." I know this sounds bad.

Is there anything I could do to show her I have changed? What would it take for you to forgive your ex after spying on you?