Visiting Belgium with a Schengen multiple entry visa from France

The answer is yes, theoretically. You first arrived in the country that issued your visa and followed your itinerary (that's a good thing). You returned to your country without overstaying and this helps to establish you as a bona fide visitor (that's a good thing). You have the opportunity to make a visit wherein your accommodations have been prepaid (that's another good thing). You have a cogent rationale and a premise that is relentlessly coherent (i.e., economic conditions).

The border official has the option (but not the obligation) to challenge you to produce onward travel arrangements to France. If this happens you can point out the things mentioned above. Bring all your evidence and and you will not have a problem.

In particular, the border official has the right to ask for one or more of these during the landing interview...

• confirmation of the booking of an organised trip or any other appropriate document indicating the envisaged travel plans;
• a document from the establishment providing accommodation or any other appropriate document indicating the accommodation envisaged;
• reservation of or return or round ticket In general a paid return ticket is not required but can be requested in exceptional circumstances.
• proof of financial means in the country of residence
• proof of employment
• proof of integration into the country of residence: family ties; professional status.

As always, any interaction with a border official is governed primarily by personal impact and articulation skills.

Of course, this is the purpose of the Schengen visa: it allows free travel in the Schengen countries as much as you want, within the dates indicated in the visa. And if the visa is valid for long-term like 3-6-12 months, then 90 days within 180 days (total of schengen stay) each time, i.e. max. 180 days in a year.