The phrasing « je parle (le) bon français » does sound odd if you want to say “I speak French well/fluently”. As long as the adjective “bon” qualifies the noun “français”, it sounds as if there are multiple variants of the French language and …

I speak a sophisticated / refined / good type of French (among them) – that is, the kind of language with impeccable grammar, a more elevated level of vocabulary etc.

Rather than tinkering with the noun “français” by adding some adjective, you usually use an adverb like “bien/couramment” instead to have it qualify the verb “parler”:

Je parle bien/couramment français.

On the other hand, if you do have the meaning of “a sophisticated type of French” in mind, you can grammatically say something like:

Qu’est-ce que ça te coûte de parler le bon français de temps en temps ?

… with a definite article “le” preceding the adjective “bon” – preferably in Italic.

You can also say the following with essentially the same meaning:

Qu’est-ce que ça te coûte de parler en bon français de temps en temps ?

Note: An (in)definite article cannot be placed immediately following the preposition “en”. A similar example: « avoir une bonne santé » vs « être en bonne santé ».

Last but not least…

Je parle un bon français. === Je parle bien français.

Adding an indefinite article instead of a definite article works, too, but note the difference in meaning between the two: « parler le bon français » vs « parler un bon français ».

The definite article serves to impart a general, global sense to the noun “français” – in that the notion of « le bon français / a sophisticated type of French » is something recognised and shared by everyone in society, not just by you.

…Whereas with an indefinite article, the noun “français” takes on a personal nature, the focus now being on what level of French proficiency you are currently at: « un bon français / a good command of French ».

I just want to add that “Je parle bon français” is wrong for exactly the same reason that “I speak good English” is wrong for the intended sense. In both cases, it is your speaking ability that is at stake, so the word you need to modify is the verb, which is modified with an adverb (bien/well). If you use the adjective (bon/good), then you are qualifying not the verb but the noun, and are referring not to your fluency but to your use of an elite dialect of the language. That distinction between an adverb modifying a verb and an adjective modifying a noun is both bon français and good English.