You need to check with your Indian operator to know exactly how much roaming would cost and decide if the convenience is worth that much.
In the European Union, international roaming charge are regulated and reasonably cheap in my view (0.24 €/min for outgoing calls and 0.07 €/min for incoming calls). Different operators might offer better deals and can also in principle charge whatever they want on their home network but you can expect this to be about right at of early 2014. Switzerland is not included in this scheme (but not always more expensive for EU-based SIM).
Obviously there is a trade-off between price and convenience but if you mainly want to place short calls in the countries you are visiting and the EU roaming charges are acceptable to you, you can pick up just about any pay-as-you-go SIM card or phone with international roaming when landing in Paris and use it in all the other countries with minimal hassle (no need for extensive research or a SIM card per country).
Regarding calling cards, the way they work is usually the following: You call a toll-free or cheap number, you dial the code on your card, a voice tells you how much credit is left and asks you to dial the number you want to reach. Sometimes you are connected directly, sometimes you get an automatic call-back on the phone you used to initiate the call. To use a calling card, you still need a phone and phone booths are not so common anymore in some areas. I think hotels or roaming mobile phones can also charge you something even for toll-free numbers (i.e. they are only free when being called from a landline/phone booth, read the fine print).
Those cards already existed before mobile phones became common and are were promoted for long calls to countries in Africa or Asia for people who have family there. If your purpose is simply to book things during your trip or make short calls to plan visits, it would not seem a good choice but if you want to have long calls with India, it might be cheaper. There are also a few mobile operators targeting this market (e.g. Lebara) but I wouldn't know what the differences are between them. For this particular use, none of the solutions seem really cheap and Skype on a free Wifi might be an attractive alternative.
Finally, if you are visiting friends or acquaintances, do ask them, in some countries like France it's quite common to have an ADSL package that include free calls to many countries and they might not mind letting you use their phone.
