She has . . . . . . . . French name but she’s English, not French. A. a B. an C. the D. no article

The correct answer is D. no article.

The reason is that the name is not specific. It could be any French name. If the name were specific, such as “Marie”, then we would use the definite article “the”. For example, we could say “She has the French name Marie, but she’s English, not French.”

The indefinite articles “a” and “an” are used when the name is not specific. For example, we could say “She has a French name, but she’s English, not French.”

In this case, the name is not specific because it is not clear which French name the woman has. It could be any French name. Therefore, we use no article.