Somehow bon marché and économique sound positive to me, as some kind of praise. In English cheap has a connotation of not good. It can be used for an expensive thing but not well made. Am I just mistaken in my impression of bon marché, or does it really differ in French and English?
You're right. Neither bon marché nor économique are used in the same way as cheap is used to belittle the quality of the goods. Économique definitely has a connotation of praise, maybe bon marché less so but neither is used in a deprecatory way.
Remember though that these words are not really interchangeable.
When you use économique you are implicitly saying there are more expensive ways of spending your money. The point of view is that of the content of your purse. Économique is used in the same way as the English "economical".
Bon marché is used to qualify the price of the goods. And of course if you buy something that is bon marché it is économique for your purse.
Bon marché originally was à bon marché (1171) (meaning you are making a good deal).
By the way, Le Bon Marché was the first French department store.
In my mind, bon marché is indeed much more of a praise in French as is 'cheap' in English. You still get what you pay for, but the emphasis is on the money you save, rather than on the poor quality of what you get. The same stands for économique.
As you mention it yourself, 'cheap' can be used to describe sheer quality, whatever the price may be, whereas économique cannot be used in that sense.
That being said, I'd probably use bon marché to translate 'a poor man's (something)' (and I'm not sure what consequences it has :)