As others have rightfully pointed out: there is no unique European greeting custom. Consequently there is no universally acknowledged strategy to avoid awkward situations. I however agree with my fellow travellers here: shake hands with strangers and with people to whom you are not close.
Physical contact is strongly linked to intimacy and familiarity. If however you become close to someone and wish to greet them with something warmer than a hand shake, then follow their lead. Or ask for the correct protocol. After all they are your friend so they'll understand your confusion.
What About France?
This is all nice and true and works in princple. What about France?
The easy rule for men: use handshakes and everything will be fine. Wherever you are: at the bar, at work, in the sauna, shake the hand and be happy.
With women however things are slightly more complicated. One simple rule is: when doing business, or when you are in a formal setting, always use handshakes.
Informal Get-Outs with (Female) Friends
However this changes completely when meeting up with friends, or friends of friends. The rule here is simple: greet the men with a handshake, greet the women with two kisses on the cheek. This applies if such women are already your friends, or if you are meeting them for the first time. This is termed faire la bise.
I have witnessed this in groups of all ages and between people of all regions across France. Moreover it's always fun when a male foreigner pulls his hand out for the classic shake and ends up bumping into the woman.
Needless to say this makes the greeting and goodbye phases not only very long in duration but also somewhat complicated with the combinations of kisses to give growing with the number of females in the group.
At the Workplace with (Female) Colleagues
Yes I have worked in France, and yes I have witnessed daily cheek kisses between male and female colleagues. Of course this applies to colleagues that are friends, whilst it does not apply between people that can't bear each other (but neither does the handshake) and subordinates wishing to maintain a formal relationship.
I also have some interesting stories regarding the official warning we all got from Human Resources during the H1N1 pandemic alert of winter 2009, explicitly mentioning la bise and how its practice should be limited in the office, but I'll leave that for another day.
Avoiding Awkward Situations
Since the OP explicitly mentions avoiding awkward situations in which one party expects one type of greeting and the other does not deliver, here I thought I would suggest a strategy often used in the real world.
If unsure you ask:
on fait la bise? Meaning: should we kiss it out? It breaks the tension and allows you to get a feeling of what the other person thinks is the way to go. This applies both if you are a man travelling France or a foreigner woman who is not used to kissing strangers on the cheek, twice.
Now I don't want to say: go out there and kiss every single French woman you meet. So if in doubt wait for her move. But be prepared, she will most probably expect two kisses on the cheeks.