We have asked Madame Mathias if she will sponsor our French club.
Here's why:
* Present perfect tense is used to talk about actions that started in the past and continue to the present or have an effect on the present.
* The sentence implies that the action of asking has already happened, and the result of that action is still relevant (we are waiting for her answer).
* We use "have" + past participle ("asked") to form the present perfect tense.