I cannot think of any equivalents for these terms in American English. In America, we have three major summer holiday periods: Memorial Day weekend in late May; Independence Day and its weekend in July, and Labor Day weekend in early September. Of course, people take summer breaks at other times in June, July and August, but there is no word to distinguish people who prefer one month to another.

I cannot think of an equivalent word in British English either for someone who takes holidays in July or August. We just refer to it as the summer holidays or summer break. We also refer to other periods of holidays by the seasonal terms like winter, Christmas and Easter holidays or break.

The holiday culture in North America is so different than France, you won't find a similar word for "juillettiste" or "aoûtien". We only take 2 or 3 weeks vacation (on average), and not the 4-5-6 weeks which is so common in France. When I was working I would have loved to say "I'm taking July off, see you in August" haha. But I could only really do that sort of thing near the end of my career. In my country of Canada, the only "holiday" word I can think of is "snowbird". That's a person who flies south to the United States or Mexico for a vacation during our winter. We also have "lake people" to describe people who own a cabin on a lake somewhere. For example, "I'm a hiker but my parents are lake people for most of the summer, and in the winter they're snowbirds".

@July, indeed it seems it can't be translated. But as @John suggested, "July holiday-goer" could be a suitable equivalent in English. We have indeed those two words mainly used by the medias to deal with people going on holiday. We also talk about the crossover between Juillettiste and aoutien on roads / train stations on July 31st/August 1st.

No, we don't have any words to differentiate what month of the summer we go on vacation. We just say "I am going on vacation in July/Aug. We could also say I am taking my summer vacation in July/August. Interesting that you have these words.