Actually with this law, if you get disconnected, let's say for 6 months (add that to a fine), you still continue to pay for the service to the providers.
Some people here in france began using anonymous VPN connections like iPredator or Relakks.
And the funny thing is that the governement acted on impulse and told the press they'll make another decree/law to punish ISPs who don't cooperate... but failed to act upon that decree/law requiring an agreement for the compensation of the ISPs.
I'm not sure about the SMTP servers, I believe they use the ones of the ISPs from what I recall reading in the french net press. Tho the first email received by someone has been dissected and they used an adress @ "hadopi.com" as sender, so I'm not sure... Anyway Hadopi has everything to send the emails themselves if they want, yes...
Hadopi's required / they say they need to send 25 000 notices per day I believe, but actually send 100 for this time. Also, "Free" handed the IPs on paper instead of providing the data digitally like every other provider. And yes another provider urged the governement to act to make "Free" comply as they sensed "Free" was gaining a little bit more popularity with this trick.