Writing to French girls is one of the world's finer arts and should be attempted with the utmost care.
Like poker, it takes 5 minutes to learn and 2 lifetimes to master.
Begin your article with "Chère", meaning "dear" or "Très Chère", meaning you really want her to understand you feel close to her (not "Cher" as that is to be used when writing to a man) and then write the name of the lucky girl who will be recieving the letter. If it is not known, write "amie" meaning friend; another subtle variation : "Très Chère Amie".
Next, start your letter. French girls are not as promiscuous as they are made out to be, so make sure you are honest, and ask a lot about her. Begin with Bonjour, or salut (Hello/Hi), then write some questions (a standard one is "Ça va?" meaning how are you). Note: Salut is informal and should only be used if you know her.
People in European countries are generally interested in other cultures, so make sure you say a bit about youself, or she will think you're boring (not the daring entrepeneur that you really are).
Finish the letter with a simple "Au revoir" (Goodbye). If you are desperate write "Ecris-moi vite!", meaning write back soon. If you are more daring, which I am sure you are, try a variation, like "Au revoir, ma chérie. Je t'adore." meaning, "Goodbye my dear, I love/adore you". However, do not go all lovey-dovey on her straight off; she might question your motives if you do. Saying "Je t'adore" is fine once you are really good friends.
Go over your letter a few times to makes sure it's all spelled correctly and makes sense.
Don't dive into a relationship too soon, you dog! Take it slow. Bear in mind that the French are people too, not the cheese-eating surrender monkeys they are made out to be.
Get the girl's address. It helps a lot if you have it.
Learn some French. Google Translater is NOT good. Invest in a French-English dictionary.
Take some French lessons if you can. Writing to the girl can be a great motivation to learn the valuable language of love.
Remember, French girls are worth time. Don't dive into it.
Make sure you're saying the right things. She will think you're an idiot if your letters make no sense (this is why google translator is so bad).
Avoid saying "Je t'aime" unless you are hopelessly in love with the girl and want her to know.