'Does Fluorine has more s-character?' is ungrammatical. That is because when you make questions with does, this does takes up on itself all the grammar categories of the predicate verb — the present tense, the 3rd person, singular, leaving the predicate verb stripped of all the categories, in the infinitive form.

He speaks English. — Does he speak English?

Thus, 'Does Fluorine have more s-character?' is absolutely correct. If it sounds "unnatural" to you, you can express possession in a different way, for example:

Has Fluorine got more s-character?

Does Fluorine possess more s-character?

or even

Has Fluorine more s-character?

which is the classical way to say it in the Modern English, although in the recent years such usage has declined drastically.

'Does fluorine has more s-character?' is ungrammatical. That is because when you make questions with does, this does takes up on itself all the grammar categories of the predicate verb — the present tense, the 3rd person, singular, leaving the predicate verb stripped of all the categories, in the infinitive form.

He speaks English. — Does he speak English?

Thus, 'Does fluorine have more s-character?' is absolutely correct. If it sounds "unnatural" to you, you can express possession in a different way, for example:

Has fluorine got more s-character?

Does fluorine possess more s-character?

or even

Has fluorine more s-character?

which is the classical way to say it in the Modern English, although in the recent years such usage has declined drastically.