What To Do
Natural nails
Softly white tips
Flattering oval shape

Polishes I Like
OPI - It's really worth every penny if you ask me.  Premium polish doesn't goop up in the bottle for me the way drug store stuff does even tho to be fair, you can actually find OPI in drug select drug stores, so check, but it's not cheaper, just easier to find.  Otherwise try a manicure center or day spa that sells retail at the counter.

Removers I Like
I use a combination of harsh and non-harsh removers, depending on the step of my technique and how much of a hurry I'm in.

Tools I Like
I really don't use much in the way of tools.  I use a fat glass file because I find it easier to control and quite precise.  I usually do a quick soak and push back of cuticles then I cut them off.  That's about it really, there's not much to it.  Good quality polish, a good quality glass file that's not made for fake nails (too rough) and a corrector pen is about all you need.
 

When a lot of people think of "french manicure" they think of these silly looking nails that people actually PAY to have stuck on the ends of their fingers.  Fakey Fake acrylic tips that look ridiculous and cheap.  The following pic was actually meant to be an advertisement for doing your nails, if you can fathom it.

French manicure done RIGHT looks lovely, is shaped naturally and the length is natural as well.  Maybe a very talented technician can shape tips this nicely, but I prefer to just use the actual natural nail and enhance it's length with nothing more than a nail polish technique that involves painting white just a smidgeon further back than it's natural line.  That way really short nails can look nearly twice as long so you get to have short nails AND good looking uniform length nails all at the same time.

Even if one of your nalis is broke clean off at or even below the white crescent, you can still fudge it with the white polish at the tip and it will blend in with the rest and look great like that "perfect 10" look you want.

Here is my before/after and as you can see the nails are very short, half of them are broken clean off (but filed smooth as a prep step) and yet after the quick and easy classic french manicure, they look uniform and lovely.

How to do it
You simply apply a couple of coats of white polish to the tips.  Trust me you will get good at this very quickly but not the first time!  Then use a corrector pen to neaten up the inside crescent shape for each nail, making sure it's neat and clean.  I dip a corrector pen in acetone to make the job very quick.  Then apply two coats of a pale pink tint over the top of everything and you're done.  Spray with shea butter or almond oil finishing spray for a quick dry and great smell.  Every two or three days apply a clear coat top to make this manicure last a week.

The photo doesn't really do this well-groomed look justice.  You will find yourself looking at your nails a lot when you do this.  The combination of a lengthy illusion mixed with the illusion of snow white tips is just beautiful to see, I never get tired of it.  Well done solid color looks lovely too, but for me, there is nothing quite as nice as a natural french manicure.  The real deal - not the fakey fake ridiculous thing you see so much of these days.

Technique Videos
You can get a very good look at a few different techniques by searching for "french manicure" on YouTube.

Shea Butter or Almond Finishing Spray - Any brand, this stuff smells SO good and it dries the nails FAST

Cuticles
To cut or not to cut... that is the question!  Some say just push them back or rub off with a washcloth after softening with a cuticle softener.  This is a tough call because cutting them after a quick soak and push back is so much quicker.  I don't know... what do you think?

Corrector Pen
You use a corrector pen after applying a couple of coats of white to your nail tips.  Just to clean up the inside curved line between the tip and the pink nail bed.  Trust me, after a few manicures you will not need it much, but it's great for those little mistakes that are inevitable along the way.

TIP: If it's too weak to do a good, quick and clean job, do what I do and dip the tip into your acetone container, touch to a folded up paper towel and then correct away.