There is no visa centre for Spain in my home city, can I apply to France instead?

If you planning to visit two or more Schengen countries, you should apply for the visa in the embassy/consulate of the country you will be residing in for most of the traveling days, so you have all rights to apply for a visa in France Embassy since you planing to be 5 days in France, but purpose of visit of course can't be conference in Spain. Just apply for tourist visa in France and provide a proof of accommodation in France for your entire stay in Schengen area, then travel to Spain on conference and other countries. Nobody will cause you problems, becuase with your Schengen visa you have right to travel to other countries in Schengen area.

It seems we know the essential purpose of your trip is the conference in Barcelona. If that is so it determines where you are supposed to apply - ie Spanish visa centre, regardless of how long you spend in other countries.

From Article V of REGULATION (EC) No 810/2009 OF THE EUROPEAN PARLIAMENT AND OF THE COUNCIL of 13 July 2009 establishing a Community Code on Visas (Visa Code):

1. The Member State competent for examining and deciding on an application for a uniform visa shall be:

(a) the Member State whose territory constitutes the sole destination of the visit(s);

(b) if the visit includes more than one destination, the Member State whose territory constitutes the main destination of the visit(s) in terms of the length or purpose of stay; or

(c) if no main destination can be determined, the Member State whose external border the applicant intends to cross in order to enter the territory of the Member States.

Attending the conference is good reason for making the trip. Mention of it strengthens your application and can be expected to improve your chances of being granted a visa (by Spain).

Balance the days in France and Spain and neglect to mention (unless asked, of course!) the conference and France should not refuse (decline to consider) your application on the grounds that you have applied to the wrong visa centre. France would be the Member State whose external border the applicant intends to cross in order to enter the territory of the Member States.

Go a step further and arrange more days in France than in Spain (or anywhere else Schengen) and France should still not refuse your application since it would be the Member State whose territory constitutes the main destination of the visit(s) in terms of the length ... of stay.

However, if France finds out about the conference it might decide for itself that that is the real ('main') purpose for your trip and, for failing to declare it, reject your application under 8. the information submitted regarding justification for the purpose and conditions of the intended stay was not reliable (same link, page 55).

It is up to you to weigh the risk of not obtaining a visa, in time, from either centre (and the possibility of a black mark against you) against the cost/inconvenience. That may sound bleak but if, say, you are very confident France would issue you a visa were there no conference involved at all (for example, there are no doubts about itinerary, subsistence, insurance) it could be a risk worth taking. For example, if this is not the first time you have applied for a Schengen visa and have never been refused any visa.

The risk is not so much that you may be denied entry at Paris but that France won't issue you a visa.

In theory, if the purpose of your trip is a conference in Spain, then Spain is your main destination regardless of how many days you spend in France. However, it is most common to judge the main destination by the number of days spent in each country. Therefore, the French consulate may accept or reject your application depending on how much weight they give to the conference.

If the French authorities decide that Spain is your main destination, they are supposed to return your application along with the visa fee and instructions to seek the visa from Spain (I do not know whether they will return the processing fee). The costs of a rejected application, therefore, are relatively low.

Your best course of action, therefore, is probably to modify your itinerary so that you are spending more days in France than in Spain, but be aware that it's possible you'll still have to apply to Spain in the end.

If you do not have time for a second application, then the more certain course of action would be to apply to Spain.