Is 'pojkvän' a term that could be used (with no connotations) for a middle-aged male partner of (e.g.) 10 years? Or is it used more in the sense of teenagers?
In (British) english, 'boyfriend' can be used for any age and relationship length, but the connotations are that of younger people (e.g. teenagers) or a less serious relationship (e.g. less than ~2 years). Personally I refer to my partner of 8 years as 'partner' because he's not a boy and we're pretty committed.
Older couples in Sweden struggle with the terminology as well. I'd say "pojkvän" has exactly the same tendencies as "boyfriend" to be used for younger people, but just as in English you can hear it used for any age group, in Swedish you do sometimes here 65+ year-olds in retirement homes talking about their pojkvänner.
It sounds very normal to me! Actually a lot more natural than "Nej, jag har inte en pojkvän". It almost sounds like that second sentence is implying that I have something else, just not a boyfriend. Like: "Nej, jag har inte en pojkvän. Jag har en flickvän" (No, I don't have a boyfriend. I have a girlfriend)
« Nej, jar har inte en pojkvän » isn't correct in Swedish. « Jag har ingen pojkvän » is completely normal and I guess they could say « Jag har inte någon pojkvän » but I'm not sure about this one. Both sound really weird when translated to French too, but Swedish is weird sometimes...