If by customs you mean passport control then no you won't since both countries are Schengen.
You will need your passports with you as the airline may check them and you are required to have them.
You will pass through customs - the green channel though which basically means walking straight out.

This will be considered a domestic flight - so no customs. You will, of course, need your passports as proof of identity and to get through security.

The only point where you may have to show your passport will be at check-in.
You don't have passport control at security (but a check if you got a boarding pass).
There will be no passport checkpoints in Venice or Paris.
Intra EU flights use the same baggage claims facilities as those from elsewhere. So you don't have the luggage carousels right next to the exits as for domestic flights within the US.
So you will walk out thru the same customs exits as non EU travellers, but can use the blue lane (for arrivals from the EU customs union) or the green exit if there is no dedicated blue exit.
If you have checked luggage, the tags will be color-coded so customs officials can see that you have been traveling within the union and are allowed to bring more goods than you can carry.
Spot controls may happen nevertheless, and customs officers have the right to inspect your luggage (and immigration officers can check your passport very randomly) even if you arrive on an intra EU flight.

Just to be clear about your question, customs is for luggage/baggage, etc.
Immigration is for people, passport control.

I don't think you understand what Customs is. It's about declaring items you've bought in one country when traveling to another. The vast majority of travelers never "go through Customs." You're probably talking about immigration/passport control. Unless you are the target of a random search, which can happen, you won't have to deal with it.

The only point where you may have to show your passport will be at check-in.
You don't have passport control at security (but a check if you got a boarding pass).
There will be no passport checkpoints in Venice or Paris.>>

cowboy, you have to be joking. on our last exit from CDG, our passports/boarding cards were checked no less than 9 times, often by people who had watched other people check them seconds earlier.

this included security which everyone has to go through - I reckon we were checked 4 times from entering the security queue to the point at which we went through the scanners. we started counting so ludicrous was it.

That is indeed a pretty weird exemption from the rule.
I fly to a handful of airports on a monthly basis, like Brussels, Vienna, Barcelona, Berlin and Munich ... and you never show your ID card or passport to anyone but at check in. Or not even there if you got the boarding pass sent to your mobile.
Yet, it is some airlines's or airport's home-made rules which no one can foresee.
I guess airports are modern day funny farms where they can send all people that would have problems to find a job in the real world and have them come up with brilliant ideas on procedures and organisation.

cowboy - we were pretty surprised too, hence starting to count how many times it happened. they even wanted to see our passports before they let us approach the check-in desk.

it did indeed feel like some sort of bizarre french job-creation scheme. the best bit was after we'd shown both passports and boarding cards at the departure desk, another person [who'd been watching and was standing about 2 meters away] checked it all again.

at our local airport, [Bristol] apart from check-in, they usually want to see our passports and boarding cards at the entrance to security, and again before they let us on the plane at the departure desk.

Thanks everyone for you input. I will have my passport, I was wondering about baggage and customs. Your replies are all very helpful. I'm aware of security and random searches. I was just wondering since I wasn't sure if traveling between Italy and France was considered as traveling between countries.

Such confusion over a simple matter and confusion over terminology..

Most of the eru countries (but not all, Ireland and the UK are not part of this agreement) have agreed on a routine basis to end border controls among all the countries parties to the agreement. Italy and France are part of the agreement so there are, as a matter of routine, no border controls. Hence a flight from Italy to France is a flight covered by the agreement called the Schengen agreement. Therefore there are no routine border controls at the airport in Venice and at the airport in Paris. There was some controversy about two years ago when France became upset at the number of how shall I phrase it undesirables crossing from Italy to France and began more strict checking of passports but that quickly passed.

Customs has to do with what you are bringing into a country and allowances throughout the eu are not completely standard but for the most part tourists do not exceed the allowances. But technically, you do go through customs leaving the area where you pick up your baggage but in almost all cases, there is a lane for nothing to declare. That is passing through customs and sometimes there are spot checks.

Lots of people confuse the two issues.

>>Such confusion over a simple matter and confusion over terminology..<<

I don't believe the OP was at all confused. She asked about "Customs" and that is what she meant. She explained she was asking about their luggage . . . i.e. "Customs"