visa – cross-border travel by land

When leaving the UK and entering France, an entry check will definitely be carried out. For the Eurostar train do both in the UK (French officials may do so). Otherwise, your Schengen visa will be checked on entry to France. (TO EDIT: Not right; see comment below. Only the arrival by plane is possible in France. Other means of transport from England will be checked on departure.)

What you have heard is the Schengen zone. Many European countries have abolished immigration and customs controls at their common land borders. Therefore, the journey by bus / train from France to Germany, Belgium, Spain and Switzerland will be as uneventful as the trip from New York to Connecticut.

(SECOND EDITING: I missed the testimony of the OP that he is an American. If he's really a US citizen, he does not need a Schengen visa at all for a tourist or business visit.)