Est-ce que tu veux que je parle français ? is correct.

The grammar you need to know here has to do with subordinate clauses. The construction “do you want me to speak” just doesn’t exist in French; you have to say, literally, “do you want that I speak.”

Que is a conjunction, and the verb after it may be the indicative (normal present tense) or the subjunctive, depending on what comes before que. With vouloir, for example, you need the subjunctive, but in this case it doesn’t matter because the first person indicative and subjunctive of parler are identical.

Est-ce que tu veux me parler en français ?

This means “do you want to speak to me in French?”

In addition to the other answer, you can express that as following:

• Voulez-vous/Veux-tu que je vous/te parle en français ?
• Souhaitez-vous/Souhaites-tu que je vous/te parle en français ?

Note that unlike with English language where the name of a language is written with the first letter in capital (Italian, English, German …), in French language you must not do that (italien, anglais, allemand) because, for instance, Allemand means a German (citizen) whereas allemand means either the German language or something related to Germany (adjective)

I would rather use a collective:

• Vous préférez qu’on parle français ?

“Do you want me to speak French?” seems quite an idiomatic turn of the English language, don’t you agree ? So as to say it expresses what is called in French ” le génie de la langue”, in English: “the language spirit”.

Here, the part of the sentence more particularly at stake is : “Do you want me to (do something) – that can be translated as : Veux- tu que je ? A good example can be found in : “What do you want me to do?” (Song of Mike Scott) translated as “Que veux-tu que je fasse ?”(La Coccinelle du Net) – The questioning by the singer can be more fully understood a few sentences further in the song :”What do you want me to do, Lord?”. The reliance is emphasized. Involvement in subjection is expressed. A strong will upon which to rely. “Veux-tu que je”…. A close translation is then chosen .

As Gam showed it well, to express the somehow polite, friendly, playful, sweet, (according to context), “Do you want me to” , French uses the collective form. The underlying law ruling it is most certainly to be found there : according to the French way of thinking, no one is supposed to want something from someone – if not related to a relationship of clear obedience from one to another. The French language is intent on emphasizing equality between the protagonists.

Hence, in addition to the translations suggested, some other examples of translations could be :

“On parle français ?”

“ça te va si on parle français ?”

“Si tu préfères, on parle français”

“Tu préfères peut-être qu’on parle français ?”

“Si c’est ce que tu préfères, on parle français”

“On peut parler français si tu préfères”

“J’ai l’impression que tu aimerais mieux qu’on parle français”

“Qu’est-ce que tu aimes mieux, qu’on parle français ou anglais ?”