The controlling reference point for your question is the Juxtaposed Controls Agreement between the UK, Belgium, and France. This is the legal framework that allows French border police to operate at ports and various other departure points in the UK. The French border police act on behalf of Belgium. The part relevant to your question is…
As a result of the agreements, when travelling from the UK to Belgium
or France by Eurostar, immigration entry checks into the Schengen Area
take place before boarding the train in the UK, rather than on arrival
in Belgium or France. The immigration entry checks are carried out in
the UK stations before embarkation by the French Border Police (which
also carries out immigration entry checks on behalf of the Belgian
Federal Police for passengers travelling to Belgium). When travelling
from Belgium or France to the UK by Eurostar, passengers clear
immigration exit checks from the Schengen Area as well as UK
immigration entry checks before boarding the train.
The agreement has been operating in one form or another since 1994, but did not become formalised until about 2003 with the last negotiations taking place in 2011. The formal definition of these controls is contained the so-called Le Touquet Treaty.
The implementing national legislation was delegated to each country.
For a look at how the controls operate on a day-to-day basis, you can read the inspection report. Although the report deals solely with the UK aspects, it is the only known working document giving a glimpse into the internals…
The person should be asked if they can understand the person
conducting the interview and whether they are happy to be interviewed
in English (or the language being used).
Having said all of that, there is nothing in the treaty or in the national legislation (including any translations of the legislation) that imposes a language requirement on the border guards of any country. Thus from an authoritative viewpoint, there is no legal requirement for the French border guards to use the English language at St Pancras station.
Circumstantial practicality, however, dictates that the border police in forward positions speak the local language. And observation bears this out. So the answer to your question: is this a reasonable assumption? is YES (for the case of the French border police).
On a personal note, I have taken the Eurostar from London to Paris about 70+ times without speaking French until after the arrival. It’s the return journey where you get some stick.
Finally, in the more general sense, English serves as a vehicular language for all entry/exit ports in the Schengen zone, so your assumption remains reasonable for all Schengen arrival points as well.