I am planning a short 2 week trip to Europe next year and plan to travel to France, Germany and Italy. Our longest stay is in Italy, but we plan to start from Paris for now.
While I don't think you should be very very worried, it is a possibility, in that a Schengen visa by itself is not the sole requirement for entry.
For example of someone being stopped from entering, even though they had a valid visa, see this question where a person was refused entry into Germany because they didn't have proof of onward travel to Portugal where the visa was issued.
The official requirements for entry are as follows:
For stays not exceeding 90 days in any 180-day period, a non EU-country national must:
possess a valid travel document;
possess a valid visa, if required;
justify the purpose of his/her intended stay and have sufficient means of subsistence;
not have an alert issued for him/her in the Schengen information system (SIS) for the purpose of refusing entry;
not be considered a threat to public policy, internal security, public health or the international relations of EU countries.
The first two are just you having a passport and a Schengen visa; since you're staying the longest in Italy you have done the correct thing by applying there. The last two are unlikely to come up as otherwise you wouldn't have been issued a visa in the first place.
So the only thing the French authorities are going to be concerned with is the middle one - why are you entering via France, how long are you staying, etc.
The French documentation on entry is not particular specific but they do mention that they can ask for proof of finances of some sort, proof of returning to your home country (your return ticket), and 'Any document establishing the purpose and conditions of the stay' for tourists.
They may ask where you're staying in France, how long you'll be staying, and what your plans are for further travel - e.g., how are you going to leave France to move onto Germany or Italy, when are you going home.
Keep your travel info together and have it with you - accommodation bookings, onward travel bookings etc - it makes it easier to answer such questions. Your plans are entirely ordinary, though - you are entering via France because you want to visit Paris before you go to Italy, plenty of other tourists will be doing the same. Don't worry about it and answer honestly and you should have no problems.
In terms of statistics, there is some official data on refusal of entry to passengers arriving by air, separated by different grounds. The 'justification of purpose' and 'sufficient means of subsistence' reasons are separate from not having a valid visa or documents, so we can take those as cases where someone had a valid visa or didn't need a visa, but was stopped from entering anyway.
In total, France removed at air landing just under 6000 persons in 2015 for those two reasons. Given that literally millions of Schengen visas were issued in the same year, I would characterise the risk as 'very low'.
The risk would rise if you were planning to do something different to what you applied from the visa from - e.g. if you applied to Italy, got a visa, then changed plans to spend all your time in France and Germany, that would be a case where you may be refused entry.
Simply put: they don't! (meaning, not simply because the visa was issued in Italy)
Since your longest stay is in Italy, you did the right thing by obtaining the visa from them. According to the Hungarian embassy in Kosovo:
If the applicant wants to visit several Schengen countries, the application for visa shall be submitted at the Embassy or Consulate of the country in which the longest staying period is planned or is proven to be the main destination of the whole journey.
That said, bring proof of onward travel to Italy (flight/train/bus booking confirmation and/or hotel booking) to present to the French if asked. In theory, if they find out you lied about your itinerary for the purpose of getting an Italian visa, you could be refused entry and put on the SIS blacklist, making it harder to obtain a visa in the future.
That said, all-in-all it's unlikely to happen as long as your plans are genuine.