Upvote:1
Going surface travel via ferry to Italy and land travel from there, like train, will keep you within the Schengen zone, as will flying. You are not likely to see border officials although they can check randomly on and within the borders. But the company that transports you across borders can and should check your documents and if they do not trust that your visa allows you the travel they can decide not to transport you. As a general guide, the more details you have to give to get your visa, the less you can change in your travel without running into trouble.
Upvote:1
If you have valid Schengen visa issued by one of the Schengen countries, you can visit any countries which signed Schengen agreement during your visa valid dates. For example, you can get Finnish visa and then spend all the time given by visa in Spain. It's absolutely legal, however, next time you apply for Finnish visa, they can deny issueing visa to you because you haven't visited Finland with you previous visa. So it's better to enter and exit Schengen zone via country which issued visa. You can for example enter the zone in Finland, then take low-cost cost flight to Barcelona and then go back to Finland.
Upvote:3
There should not be any systematic control at the airport for flights between Paris and Athens. This means that your passport won't be stamped and you will probably not even see any border guard on the way to or from Paris by air (on the other hand, going by land through Serbia, Romania or Albania would mean leaving and reentering the Schengen area which your visa may or may not allow). Your time in France and Greece would be part of a single stay in the Schengen area, covered by your visa.
Beyond that, adding a short week-end trip to Paris in the middle of a trip to Greece should be fine but applying for a Greek visa and entering through Greece when the main goal of your trip is Paris (e.g. you spend two weeks in Paris with only a couple of days in Greece at either end of the trip to make the transfer) would be a blatant case of fraud and would expose you to all sorts of problems (including seeing your visa annulled and having to return to your country of residence immediately and probably having great difficulties in getting another Schengen visa in the future).
Even if you honestly changed your mind after getting the visa, if you spend more time in Paris that in Greece, it would look to an observer as if you lied to get in and chose to enter and leave through Greece to evade detection (in that scenario, if going to France for a long time was your plan all along, you were supposed to apply for a visa from France, not from Greece). Of course, since passports aren't always checked, it's possible to get away with this but planning to do it from the get go would nonetheless be an abuse of the system.
See also Should my first trip be to the country which issued my Schengen Visa?