Two young men with backpacks and using a white van are understood to have been spotted by private security and school staff walking the perimeter of the school and monitoring children.
A spokesman for Harry and Meghan called the actions "an extraordinary lack of judgment" after the suspected terrorist plot near RAF Fairford, with a number of American children with families connected to the base said to attend the school.
"The decision by photographers to conduct themselves in this way around a school is extraordinarily reckless," the Team Sussex spokesman said on Wednesday.
"There is a world of difference between legitimate media activity and photographers walking the perimeter of a school, stopping to look into the grounds and monitoring children as they go about their day.
"It is concerning enough that certain European paparazzi appear unwilling to respect the privacy of children at school.
"But to behave in this manner in these particular circumstances, and so soon after the incident at RAF Fairford, demonstrates an extraordinary lack of judgment.
"Whatever photographs they may have been seeking, this was not only an unacceptable intrusion into the privacy of children; it was an irresponsible and ill-considered way to conduct themselves in the vicinity of a school."
The men were initially seen separately and were subsequently observed together before returning to a white van, which police later established was a rental vehicle, with officers later determining they were international photographers working for a European press agency.
Harry and Meghan, who returned to live in the UK just over a month ago, are waiting to hear whether they will be given taxpayer-funded security.
They pulled Archie and Lilibet out of their first-choice British school in September after just two days when heavy traffic in the area meant their private security team struggled to stay in a convoy during the school run.
The youngsters are believed to have been at their new school for around two weeks.
Harry's late mother Diana, Princess of Wales, was killed in a crash after her car, driven at speed by a drunk chauffeur, was chased through the streets of Paris by the paparazzi.
