Repentance in Islam is a key concept, it's mentioned in many versus in Quran
Except for those who repent, believe and do righteous work. For them
Allah will replace their evil deeds with good. And ever is Allah
Forgiving and Merciful. [Quran 25:70]
A well-known Scholar, Salman Al-Ouda talking about Tawba "Repentance" concept in Islam,
http://www.youtube.com/watch (In Arabic)
So indeed, things are always fixable.
Moving to how you can solve the whole situation, Through my experience I found dividing the problem into smaller ones then prioritize them helping better than take them all on my shoulders
1- You would like to start with major stuff - e.g. praying - while doing some research about minor things so you can better decide what to do
2- About your marriage, as already mentioned in answers here, if your current partner is Muslim, Christian or Jew things will be fine, since i'm not fully aware about civil union contracts in France I can't tell exactly what you should do, please note that Islamic Marriage has set of prerequisites to confirm that the relationship is correct and valid.
This case might be related to yours:
3- About your daughter, if the copulation process was done while you and your partner had that civil union you should be fine, I tried to google that and I found that scholars usually distinguish between the child of "Zina" & the child of invalid contract.
Source (Arabic): www.dar-alifta.org
4- Find Islamic figures and preachers you would like to listen from, keep yourself surrounded with good Muslims, since you love your wife you can do it together, help each other, remember that your partner has huge impact on your life, hence she needs to understand everything.
I strongly advice you to visit a local Islamic organization you trust.