Speaking in Paris after talks with Togo's President Faure Gnassingbé, Hollande said Paris was checking all the information and will do all it can to find and free the kidnapped priest.
Earlier on Friday, at a conference of mayors from Francophone countries, Hollande admitted that French citizens are being targeted by Islamist groups since its military intervention in Mali but insisted France will keep on defending its values.
"Sometimes you have to stand up and fight and that’s what we’ve done in Mali," he said. "We’ve paid the price - seven of our soldiers have died there, many others have been injured. We pay the price again when two journalists are assassinated just because they’re journalists and they’re French. We pay the price when a priest is kidnapped in the north of Cameroon and taken most probably to Nigeria".
France will "do everything to secure the release of hostages", he said but added, "I can tell you we will not give any ground."
Hollande called Cameroonian President Paul Biya to discuss beefing up measures to ensure the safety of French nationals in the region where Vandenbeusch was abducted.
Analysts are puzzled by Friday's claim that two rival Nigerian Islamist groups - Boko Haram and Ansaru - worked together to carry out the kidnapping.
Security sources have told RFI that there has been no coordination between the two groups since Ansaru split from Boko Haram in January 2012.
They also point out that Ansaru usually operates in the far north-east of Nigeria, 700 kilometres from the Cameroon border.
Ansaru has been holding French national Francis Collomb for a year.
The kidnapping of Vandenbeusch, who had been working in the area for two years and had ignored French government warnings about the dangers of staying in the region, brings to eight the total number of French hostages held worldwide.
Four others are being held in Syria, another in Nigeria and two in the Sahel region on the southern fringes of the Sahara desert.