French police were already searching for the children's mother after their father filed a police reporting alleging child abduction and the woman's family reported her missing.
Media reports in Portugal said she and her partner were believed to have abandoned the two boys -- aged three and five -- with backpacks containing food and water but no identity documents.
The adults are said to have blindfolded them and pretended to be playing a game before they drove away.
The authorities in both countries stressed no conclusions could yet be drawn.
"All hypotheses are on the table," Portuguese police spokesperson Major Joao Gaspar told AFP.
French prosecutor Jean Richert said the woman's family had reported her missing on May 11, and a judicial inquiry had been launched to investigate the circumstances.
"What was surprising was that she wasn't at home, had no reason not to be there, and hadn't informed anyone," he told AFP.
The father of the boys, who is separated from the mother, "like everyone else, he doesn't understand", said Richert.
The Portuguese attorney general's office told AFP a court was investigating alongside the police inquiry, adding: "The children were taken to hospital, where they are under observation."
Portuguese motorist Alexandre Quintas was said to have found the children on Tuesday on a main road near the resort town of Comporta.
He took them to a bakery run by his family before alerting the authorities.
"We asked them if they liked ice cream," Quintas told the online outlet Observador.
"And we gave them something to eat and some toys to keep them occupied."
