En français, on dit rarement qu’on utilise un mauvais accent (qu’est-ce que c’est d’ailleurs ?)

Version la plus courante:

Je parle français avec un accent (sous-entendu: accent étranger).

Si l’on veut préciser:

Je parle français avec un accent anglais (ou anglophone).

You normally don’t state you speak with an accent anglophone as it is not the accent which is anglophone but you.

The accent is English so you would say:

Je parle avec l’accent anglais (or américain if you want to tell where you come from.)

Je parle français avec l’accent anglais.

To translate "bad accent", you’ll use fort in French:

Je parle français avec un fort accent anglais.

If you really want to use anglophone, you might say:

Je parle français avec l’accent d’un anglophone.

but that seems a little odd.

Actually, you shouldn’t worry about whether your accent is British English or American English. While there is with no doubt a difference when someone speaks English with either of these, this difference is much less noticeable when they speak French. Most native French people wouldn’t tell the difference.

Anyway, if you are talking to native French people, that might not be worth telling you have an accent in the first place as the fact will be obvious after very few words.

I’m not sure what your question is but to fit your specific problem, you could ask:

Je parle français avec l’accent américain ?
Est-ce que vous entendez que je suis américain(e) quand je parle français ?

It seems that you’re already prepared to modestly criticize yourself (or at least willing to call attention to your [bad/strong] accent & that of your typical compatriots), so why not spice up your declaration & take it to another, full-blown, self-deprecating level (As with self-effacement, I find self-deprecation, in moderation, to be endearing … regardless, it’s a whole lot better than coming across as self-aggrandizing and arrogant, but I digress).

Besides, your knowledge and use of the following idiomatic “insults” (directed only at yourself, of course) might possibly impress (or perhaps ‘disgust’?) your French audience to the point where the “issue,” probably self-perceived, of your [again, probably self-perceived/self-exaggerated] “bad” accent will no longer be of any concern.

Since yours is a North American accent, you could paraphrase an idiomatic expression as follows:

Je parle français comme une vache américaine/canadienne.

Although the unparaphrased/unedited version of this expression is, in my opinion based on its origins, insulting to Spanish Basques, to Spanish migrant workers, and/or even to Spaniards in general (not to mention all the unfairly maligned Spanish cows), the paraphrased version suggested above would probably be viewed primarily as a self-inflicted poke at yourself, but please be mindful that it could also be taken as a gratuitous slam of your country’s entire cow population.

(please note, however, that by using this phrase, especially the original/unedited version, you’d probably be seen as criticizing your over-all command of French, and not just your accent).

Had you been a Brit talking about yourself (but not to be used by a non-Brit towards a Brit [unless, of course, in response to a criticism of hockey or even worse, of curling] because, said in the “right” tone and context, it can be considered as very insulting) ….
…. you could have said:

je parle français comme un
rosbif.

(but just as with using “comme une vache américaine/canadienne” by a North American, a Brit using “comme un rosbif” might be seen as not just talking about having a [strong] British accent, but also about having other problems with the language, such as organizing and formulating phrases and grammatical structures the way they are organized in good English and not as they should be organized in good French)

(cf: “Il parle comme un Froggy mais pense comme un Rosbif,” used at the end of the second paragraph in this recent ‘ParisBouge’ interview which, if nothing else, perhaps provides another example where the use of mutual insults like “rosbif” and “froggy” is apparently acceptable.)

(in order of their appearance, the first four links above are from/lead to:
‘en.wiktionary’;
‘fr.wiktionary’;
‘news.bbc’; and
‘projetbabel’)

Vu que tu parles déjà français en parlant de ton accent, pas besoin de dire que tu parles français et l’origine de l’accent est soit, peut importante, soit évidente, tu n’as donc pas besoin de préciser d’où viens ton accent.
Pour moi la phrase correcte serait donc :

“J’ai un gros accent” ou “Je parle avec un mauvais accent”.