I'm a resident here in Italy, I had my carta identita. I'm planning to go to France end of the month this September the problem is I'm on renewal on Sept 9' and I'll wait about 2 months to get it. Is it possible that I can go to France without it or can I attach a form that I'm for renewal to present it to the inspector in the airport in France ?
"Is it possible that I can go to France without it or can I attach a form that I'm for renewal to present it to the inspector in the airport in France ?"
When going by plane, you will not see a border inspector in the first place. Flights between Italy and France are considered domestic flights, since the Schengen Area (of which both France and Italy are a part) is a single country for border purposes.
If you check in online for your flight and only have hand luggage, there is a good chance you won't have to show any ID when boarding your flight (they often only require the boarding pass at the gate for flights within Schengen)
Otherwise, simply present a valid passport when required. As stated by the European commission, check-in staff should not check your legal status, only that you're the person on the ticket. However, Ryanair notoriously violates this, so avoid them.
However, according to IATA, strictly technically speaking you are not allowed to make this trip:
Passengers with a residence permit issued by France, French Guiana, French West Indies and Reunion.This does not apply to temporary permits issued pending a first application for a residence permit. In cases where a residence permit has expired, the passenger must have a receipt of application for a new residence permit and their expired residence permit.
Passengers with a residence permit issued by Andorra, Monaco or another Schengen Member State for a max. stay of 90 days.
Note there's no mention of expired residence permits or renewal receipts being accepted for holders of non-French permits
In other words, according to this info, your trip would be allowed if you had a French residence permit, but not with an Italian one.
Again, however, when flying within Schengen airlines are not supposed to check your legal status, and you will not meet any immigration inspectors.
In short: according to Timatic, technically you cannot do this trip, but in practice you can as long as you avoid Ryanair