Your question: is the chauffage central a so called circuit specialisé, yes or no. And therefore needs a separate circuit, originating from your consumer unit, your tabléau électrique and have its own disjoncteur. Let's take a look at the regular suspects in the French NF C 15-100 electrical code.
1. Circuits spécialisés avec prise de courant: lave-linge, lave-vaiselle, sèche-linge, four, congélateur.
3. Volets roulants.
4. VMC, VMR (ventilation system).
6. Convecteurs, radiateurs, accumulateurs, panneaux radiants (electric heating).
7. Circuits d'avertissement tarifaire, fils pilote etc. Example: your relay for day/night tariff, the wiring for the contacteur jour/nuit.
8. Electricity in a separate building.
9. Other appliances outside (automatic gate).
So to conclude:
I don't see any reference in the NF electrical code obliging you to start drilling holes, breaking away bricks and plaster, and do some additional wiring. The electrical connection is a standard prise de courant, a regular socket. The chauffage central and its electrical pump are not in this list of circuits specialisés. You are free to do it, but that is something for a complete make-over. Or if you would prefer to be on the safe side, keep your central heating running, not disturbed by possible malfunctioning devices connected to the same circuit. Installing a heatpump would of course be something for a raccordement specialisé. Minor technial point: if you were to have your internet/network running on a powerline adapter, the electric pump sometimes interferes with your sensitive high-frequency signals in the circuit involved. Result: signal degradation.
Second point: only if the Consuel were to come along to control your new, or totally renovated installation, you would run the risk of getting in touch with authorities, to check what you've done. Taking note of the condition of many existing installations électriques here in rural France, probably half of France would run the risk of doing illegal things and being sent to prison.
Third point: new regulations appear. Speed limit of 30 km, where you were driving 50 km last week. Can you be sentenced for speeding last week? No. So although newer versions and updates of the electrical code make their appearance every year, this does not imply that having an older installation électrique makes you an offender, a criminal of some sort, and that you have to stay away from the gendarmerie and their possible roadblocks.
Last point: there are many urban legends around, of what an official French electrician had to say about something. Believe me, don't believe everything. Could you please be so kind as to give me the exact reference in the French NF C 15-100 electrical code, what chapter, paragraph?
p.s.: I just had a closer look at the 503 pages of the French electrical code, and not only in "the" book of Gallauziaux & Fedullo. The word chauffage central is mentioned only three times. Context: la liaison équipotentielle and the installation de mise à la terre. The earthing arrangments for metal pipes. Pages 354 and 467 in my edition. Looking at the general intro of para 771.314.2.2 on page 429 Circuits specialisés, the reasoning behind it is that "power" consumers should have their own circuit: Every household appliance de forte puissance doit être alimentë par un circuit specialisé. On the next page there is a list of examples: also the swimming pool, alarm systems and pompe à chaleur, climatisation, chaudière. Which brings me to a question of definition: is your electric pump to be considered as (part of) a chaudière? Perhaps I have been a bit too overconfident earlier in my response, but in your existing installation I don't see why you should have a separate circuit for an electric pump of say 60 or 100 watts.