I am going from Israel to Grenoble, France. I can go via either the Geneva airport or the Lyon airport. The flight to Geneva is more convenient, but it is in another country. Are there any complications in travelling (e.g. by train) from Switzerland to France? Any special border-checks, etc.? Or I just enter the train in Geneva and exit in Grenoble?
Welcome to Grenoble! It's a beatiful city.
To answer your question, there is a very cheap Geneva<->Grenoble bus, and I have never ever seen checks conducted on it. I have taken the train as well, with the same result.
EDIT: Clarification on the bus.
The bus in question is http://www.aerocar.fr/en/, departing from the airport every hour or so. There is a train station both at the airport and in the city, but the distance is walkable as well.
I have frequently travelled by train in and out of Switzerland. Border guards used to enter the train at the border, run through the train, asking one or two people for their passports (or, rarely, everybody) and getting off again. But now Switzerland is in Schengen, so the train journey should be no problem at all.
It does mean that Switzerland will be your first entry in Schengen, I'm not sure what that implies for an Israeli citizen (assuming you are).
If it's really important that France and not Switzerland is your point of entry then it's quite possible. You simply exit GVA from the French side and get your passport stamped by French immigration if they happen to be there, take a taxi to Ferney-Voltaire which is literally five minutes away from the airport. From there you can take a Line F bus to Geneva Cornavin (about 25 minutes and costs ~4€, checks at the border happen very rarely) and take a train direct to Grenoble. You will pass through customs at Cornavin, then leave Switzerland again on an SNCF train (about 2 hours), which will not be stopped or searched.
I cross the Franco-Swiss border four times a day on my way to and from work (I live in France and work in France but have to transit via Geneva using the TPG) and have had my passport checked twice in the past three months. As mentioned before, taxi's from the airport on the French side might be difficult to get as they all congregrate on the Swiss side, but tbh I landed there around 11pm so you might have better luck if you arrive during the day. Bon voyage.
It does not matter. France and Switzerland are members of the Schengen area. There will be a border control when you enter the area. When travelling between countries there are no border controls. However, the French Police is regularly patroling in international trains and makes sporadic controls. They may ask travel documents or about the purpose of travel. That's it. They preferably control dark-skinned travellers and those having a more "exotic" look.