Regulation on whether or not pest management is considered an "essential" service varies widely by country. Check out the status of each EU country on our tracker.
CS3D (France) are asking the French government to revise the list of trades authorised to continue throughout COVID-19, originally published on 15 March. See their letter here.
BPCA (UK) wrote to the UK government, who responded on 6 April clarifying that the UK's government urges anyone who can to work from home, but "where that is not possible, people should go into work where it is safe and they are not symptomatic, following relevant [Public Health England] PHE guidance". As it stands the UK's guidelines do not prohibit the continued operation of pest management. BPCA are continuing to lobby for an explicit exemption for pest management.