Pourriez-vous me dire si ce melon ou cette pastèque est meilleur aujourd’hui, madame ?

Pourriez-vous is the conditional form of pouvoir. In French, the conditional often makes a request sound softer and more polite.

• Pouvez-vous... ? = Can you... ?
• Pourriez-vous... ? = Could you... ?

Both are correct, but Pourriez-vous... ? sounds more courteous, which fits a customer speaking to a shopkeeper.

French makes an important distinction between:

• tu = informal singular you
• vous = formal singular you or plural you

Here, the speaker is addressing a woman politely in a shop, so vous is the normal choice. Using tu with a stranger would usually sound too familiar unless the situation is very casual.

The hyphen appears because this is an inverted question. In formal French, one common way to ask a question is to put the verb before the subject pronoun:

• Vous pourriez... = statement
• Pourriez-vous... ? = question

The hyphen links the verb and the subject pronoun in this structure.

Because me is an object pronoun, and in French object pronouns usually come before the verb they belong to.

Here:

• dire à moi becomes me dire
• so Pourriez-vous me dire... means Could you tell me...

This is very normal French word order. Compare:

• Pouvez-vous me dire... ?
• Je vais vous montrer...

But with a positive command, the order changes:

• Dites-moi... = Tell me...

Here si means whether / if, not yes.

After verbs like dire, savoir, demander, or voir, French uses si to introduce an indirect yes/no question:

• Pouvez-vous me dire si... = Can you tell me whether...
• Je ne sais pas si... = I don’t know whether...

So si ce melon ou cette pastèque est meilleur means whether this melon or this watermelon is better.

Because French demonstratives must agree with the noun’s gender and number.

• ce = masculine singular
• cette = feminine singular

So:

• melon is masculine → ce melon
• pastèque is feminine → cette pastèque

This is the same idea as using this in English, except French has to show gender.

For masculine singular nouns, French uses:

• ce before a consonant sound
• cet before a vowel sound or silent h

So:

• ce melon because melon starts with a consonant sound
• cet abricot because abricot starts with a vowel sound
• cet homme because homme begins with a silent h

Because the speaker is probably referring to specific fruits, likely ones they are pointing at or looking at.

• un melon / une pastèque = a melon / a watermelon
• ce melon / cette pastèque = this melon / this watermelon

So the sentence suggests something like: Could you tell me whether this melon or this watermelon is better today?

Because ce melon ou cette pastèque presents an either/or choice. The idea is that one of the two is better, not both together as a group.

So French commonly uses the singular:

• ce melon ou cette pastèque est meilleur

If the sentence were talking about both items together, then a plural would make more sense.

This is a tricky point, and it is exactly the kind of thing learners notice.

The adjective is singular because the sentence treats the choice as one fruit or the other. Since the two possible nouns have different genders:

• melon = masculine
• pastèque = feminine

French often uses the masculine singular as the default in this kind of mixed-gender either/or structure, so meilleur is acceptable.

If you were talking only about la pastèque, you would say:

• Cette pastèque est meilleure.

If you want to avoid this mixed-gender issue entirely, a very natural rewording is:

• Lequel est meilleur aujourd’hui ?
  Which one is better today?

Madame is a form of direct address, like saying ma’am in English.

Putting it at the end is very natural in spoken French:

• ..., madame ?

It softens the sentence and makes it more polite. You could also place it earlier, but the end position is common and sounds courteous in a shop or service setting.

Because when you address someone directly, French normally does not use an article.

So you say:

• Bonjour, madame.
• Merci, monsieur.

Not:

• Bonjour, la madame. ❌

This is the same idea as English direct address: Thank you, ma’am, not Thank you, the ma’am.

Yes. The original sentence is polite and correct, but in real life many speakers might choose a simpler version, especially to avoid the mixed-gender meilleur / meilleure issue.

For example:

• Pourriez-vous me dire lequel est meilleur aujourd’hui, madame ?
• Lequel est meilleur aujourd’hui ?
• Vous me conseillez lequel aujourd’hui ?

That last one is especially natural in a shop:

• Vous me conseillez lequel aujourd’hui ?
  Which one do you recommend today?

So the original sentence is fine, but everyday French often prefers a shorter or smoother wording.