It is serious and requires as you suspected and imho - a full re-wire.
First couple of crosses relate to your earth 'mise en terre' it may be that there isn't evidence that the property is earthed.
Next one is concerning the rules regarding bathrooms and shower rooms - if you have a normal plug close to water that wouldn't pass the rules.bathroom regs
More importantly initially there is evidence that some of your electrical installation poses a risk of direct contact with electricity. It appears you have live wiring which is unprotected and you have items in your installation that are obsolete or in disrepair 'vetuste'.
As the house didn't have a current power supply they couldn't actually test the circuit but it is unlikely ERDF would re-connect in it's current state.
Many older houses in France have wiring in this condition and it's only on sale that they tend to be repaired due to the new regulations which are there to protect us.
For a re-wire - the cost depends on size of property and how heavy and installation you require. How many rooms? How will the house be heated? Will you be installing solar thermal hot water?
A rough guide though from this site http://www.maisonentravaux.fr/couts-travaux/couts-electricite/cout-devis-renovation-complete-electricite/ is (m²) X (80 à 100€ HT). Don't forget that for renovations you pay only 10% TVA if you sign the declaration provided by your electrician.
From my experience please do get at least 3 quotes as they can vary, make sure the electrician is French registered and provides a copy of their assurance decennale (10 year guarantee) with their quote. This is important because if you sell the property, the responsibility remains with you if you do not have the 10 year guarantee. You will likely also need the certificate of conformity for ERDF to reconnect.
if you want any ideas of individual costs of items I can help - I'm about to rewire my house in Languedoc and I did another in 2005. That house was 140m2 - it cost approx 10,000 euro. We didn't have gas or solar but did have a lot of lighting, power sockets were as per french norms. When we sold our house (the one we'd had rewired) the diagnostic couldn't see the earth but the facture (bill) demonstrated it had been fitted and the electricians assurance decennale covered the work so the buyer and notaire were satisfied.
Hope this helps.