Under EU law the citizens of any EU country are free to move to another EU country.
If they cannot support themselves they can stay for a maximum of 3 months whilst they look for work; once this limit is hit they are breaking the law and the host country has a right to deport them.
In your case this doesn’t apply to you on both counts, you are staying shorter than 3 months and have a job. You can go and do your job from anywhere in the EU for 2 months with zero issue. Stop reading here if that's all you're interested in knowing.
This 3 months limit would be a theoretical issue for you if you were to stay longer. It’s at this 3 months limit that you can no longer legally remain under the British system but would have to switch to the French system, become liable for French taxes et al.
In practice however this tends not to be enforced, with British people in Spain being particularly infamous for illegally remaining on the British system whilst living in Spain.
Even outside of the EU there are many people who work for a company based in one country and (illegally) perform their duties over the internet from a country where they don't have permission to work. This technical illegality is rarely enforced and wouldn't be an issue unless they very publicly advertise what they are doing. But even then, (there are many digital nomad bloggers), I am not familiar with a case of someone getting in trouble for it.
Brexit is of course the big potential spanner in the works. Worst case scenario if it all blows up and we end up leaving with no deal… then it’s technically possible you could be deported come March 31st as an illegal alien with no possible legal status for being in France.
Even in a worst case no deal scenario I find this unlikely however. Travelling home immediately after the date would be complicated due to planes not being legally able to fly to the UK, but it's likely people who arrived for short visits before Brexit would be dealt with under the old rules.
Further, though this is going very into politics and opinion, I do not see this worst case no deal situation as likely. Either the deal currently being discussed in parliament will be signed, which effectively means everything remains mostly as it is with regards to Brits in Europe for the next two years at least. Or, the can is kicked down the road and the current British national sabre rattling contest continues for another few years, likely resulting in the whole thing being called off.