The French laissez-passer is only valid in France, so irrelevant to the trip to Italy. See item 5 here
Laissez-passer et approbations des conditions de vol - Ministère du Développement durable
AIC 01-2008 may be applicable to your autogyro:
A1 GEN ITALY
Navigation of aircraft whose airworthiness certificate is not complying with the ICAO Annex 8 standard
Art. 1 - General
All aircraft registered in a foreign State, not complying in whole or in part with the airworthiness standards of ICAO Annex 8 and therefore possessing an airworthiness certificate not conforming to the Annex 8, are not allowed to fly unless they satisfy the conditions listed in the following articles.
All aircraft holding a permit to fly EASA Form 20 issued in accordance with the Regulation EU 1592/2002 are allowed to fly without any further obligations.
Art. 2 - Aircraft registered in E.U. Countries, Switzerland, Norway and Iceland
All aircraft, referred to in article 1 first paragraph, registered in the European Union Countries, Switzerland, Norway and Iceland in accordance with the provisions of the E.U. Regulation 1592/2002 Annex II (a) - (d), are allowed to fly over and land in the Italian territory without the previous ENAC authorization provided that:
a. hold a current airworthiness certificate or equivalent document issued by the State of registry or by an “ad hoc” delegated organisation;
b. are conducted by pilots holding the appropriate licenses and type rating issued in accordance with the ICAO standards;
c. are operated in accordance with the limitations established in the airworthiness documents above quoted;
d. hold an insurance, in accordance with the applicable regulations, covering persons on board and third parties damages on ground for the scope(s) for which the Permit to fly is granted;
e. comply with the Italian rules of the air and the procedures published in the national aeronautical publication (AIP Italia and Notams);
f. do not fly over towns or crowded areas;
g. are not involved in public transport, school and aerial work kind of operations;
h. any passenger is informed that the aircraft is not type certificated in accordance with ICAO Annex 8 standards.