Always have some cash on hand, enough to pay for the restaurant if they don't accept your cards or any cards at all. Spread the money among people in your travel group.
Warn your bank so they don't block your cards and bring two different cards if you have them (some circuits like american express aren't accepted everywhere, mastercard or visa are very widespread).
Paris and Rome are typical for pickpockets as are all touristy areas in big cities. Pay Pay attention when withdrawing money from ATMs.
I suggest you look on google for the videos of roma kids crowding a guy withdrawing money from an ATM in central paris, they took all his money. Read up on their scams and distraction tactics too and learn how they look (there are hundreds of videos and photos really), seeing this before will make you more aware and less gullible. Needless to say, don't even stop for beggars. Remember that most begging acts are either organized rackets or consequence of illegal immigration. Same goes for people walking up to you and asking questions, people from the countryside often fall for these tricks the first time (like "I'm about to miss the train and I need 2 more euros to get the ticket"), so if it happens to you, stop 5 seconds and look at their clothes and how they look. Roma women dress in a very typical way and their indian origins are visible so they're easy to recognize after a while. Avoid automated ticketing machines if you see them "helping" people, unless you want to argue over the change.
For small payments, using the card is more rare but if you ask they usually do it, in Italy forget about using credit cards for street food or even some small shops because many don't have a machine. Depending on the size of your group you need a minimum amount of cash because it can happen that some restaurant doesn't take credit cards, or doesn't have a working POS machine and you don't want to waste time looking for an ATM.