When you don't know about the marital status of a French woman, you can write to her "madame". She won't be offended. Anyway there is no real equivalent to 'Ms' in French.
"madame"
Madame.
Unless the woman specifies otherwise, always address correspondence to Ms.
Traditionally, in French a young or unmarried lady is referred to as "mademoiselle". A woman or married lady is referred to as "Madame".
In French, "Mrs. Jones" is translated as "Madame Jones." The term "Madame" is used to address a married or older woman, similar to "Mrs." in English.
Frau
Mrs. is a title of respect that may be used to address a married woman. Ms. is preferable, especially if you do not know what the woman's preferred title is, or if you do not know the marital status of the woman.
Typically, a married woman is referred to as Mrs. Whomever in writing. It is pronounced as missus, and signifies that the woman is no longer single.
Frau
You can address an unmarried woman as "Ms." just as well as a married woman. In a situation where you are unsure of the marital status, "Ms." is a safe form of address, and avoid "Miss" and "Mrs."
The usual term to address an unmarried woman is 'mademoiselle'. When the marital status is not relevant (for instance in business relations), or when the person is obviously old enough to be married, it is quite common to address her as 'madame', as is standard for women who had been married in the past.
The prefix "Mme" is short for "Madame," a French honorific used to address a married or older woman. It is equivalent to "Mrs." in English.