Who should apply for the work permit, the french tour promoter or the foreign producer?

Your question does not explicitly mention it, but we assume you have concluded a contract of sale with an entertainment promoter established in Quebec for the purpose of presenting Quebec artists in France.
In addition to obtaining a residence permit from the French embassy or consulate, foreign artist are also required to obtain a work permit to work in France.

If the foreign artist does not reside on French territory, the rule governing the work permit is that it is up to the employer to apply for it, whether he is based in France or abroad. In live entertainment, the application should be filed by the employer, producer or tour promoter.

Nb > It is generally accepted practice that the artistic agent, if licensed by the ministry of employment, he being the artist’s agent rather than employer, can accomplish the necessary formalities involved in applying for a temporary work permit.

If the artist already resides on French territory under another valid type of residence permit or a short-stay visa (less than 3 months), he should apply for it at the préfecture where he lives.

You say that the Quebec production firm wants to employ the artists as salaried workers and invoice you for the service. It is therefore the Quebec production firm that is considered the employer and it is up to the said firm to initiate the work permit application process of the artists are not already resident in France (see News, Issuing temporary work permits to entertainment artists and technicians ).

However, before the service commences, you must ascertain that the salaried worker is duly in possession of a permit or document permitting him to do salaried work in France. Hiring foreign salaried employees who are not in possession of a valid work permit is punishable by a 5-year prison sentence and/or a fine of 15,000 euros for each foreigner concerned (See Foreign artist – residence and work permit ).

Moreover, as part of the fight against illegal labour, if the contract exceeds 3,000 euros, a promoter based in France is required to carry out a number of checks, and among other things you should ask the Quebec production firm for (see Foreign artist seconded under a sales contract entered into with an entertainment promoter based abroad: the French promoter’s obligations and responsibilities) :

•  either documents proving that the contracting party is in order with respect to his social obligations. For countries that have signed a bilateral agreement on social security with France, which is the case for Quebec, you should be given individual certificates of secondment issued by the organization in charge of the social welfare scheme in the country of origin (See Promoter based in a country signatory to an agreement with France );
• or documents proving that the contracting party is in order with respect to his tax obligations; 
• plus a sworn affidavit from the contracting party certifying among other things that the salaried workers are  permitted to work in France (or will be at the time the service is performed) and that the work will be done by salaried workers legally employed with regard to articles L143-3 and L320 of the labour code (pay slip, statement of recruitment) or equivalent rules in the country they are attached to.
  

     lastly, if registration in a trade register is mandatory in the country where he is established, you should also ask for: either a document issued by the authorities of the country certifying such registration; or an internal document (quotation, advertising document or business correspondence) bearing the company’s registered or trading name, full address and type of business registration, or - for companies pending registration - a document dated within the last 3 months and issued by the authority of the country holding the said register, certifying that registration is pending.