@Ww
It would appear that the suspect emigrated to Italy in 2012. He served a prison sentence in Italy for arson and has been convicted for a crime in Tunisia, presumably before 2012. Maybe that's why he didn't want to go back to Tunisia.
I don't think Tunisians have the right to go to France, although Algerians had the choice immediately after independence. Historically, Tunisia had as many ties with Italy as it did with France and the old Tunisian government encouraged people to emigrate, but monitored its overseas citizens to make sure they didn't involve themselves in anti-government initiatives.
Interestingly, this man left Tunisia at the beginning of the 'Arab Spring' season before IS moved in. He was probably radicalised in Europe rather than sent by IS. Tunisia is the most secular of all the Arab states, although there are still groups within the country which resent the secular constitution.
He has been arrested three times by the German police, but released on each occasion, despite being known to intelligence services. He entered Germany in 2015 and his asylum application was rejected. However, he couldn't be deported, because the Tunisians refused to recognise him as a Tunisian citizen.
I'm sure there's more to this, but you have to ask yourself what the heck the German police and intelligence services were playing at. I think it's unfair to blame Merkel's policy on immigration, because he was already in Europe before the migrant crisis developed and was already on the radar. On the face of it, it seems like a failure by the authorities to monitor him.
Let's hope he is caught without any further loss of life.