He awarded Xavier Jugelé, 37, the Legion of Honour, one of France's highest honours.
The two candidates to succeed Mr Hollande, Emmanuel Macron and Marine Le Pen, both attended.
They will face off at a second round of voting on 7 May.
Mr Jugelé, 37, was killed with a Kalashnikov rifle while on duty on the Champs Elysées avenue last Thursday, The main suspect is convicted criminal Karim Cheurfi.
"Once again France has lost one of its bravest sons," Mr Hollande said. "Once again the Republic has lost one of its most valuable guardians."
He said France's struggle against Islamist terrorism was "a fight that is going to last, a fight that will be waged until the threat is completely neutralised".
Mr Jugele's partner, Etienne Cardiles, gave a moving tribute to his loved one, who had campaigned for gay rights and volunteered in Greece to help with the migrant crisis.
"I suffer without hatred," he said.
The issue of security sharply divides the presidential candidates, who were appearing together in public for the first time, though discreetly.
They were among a large group of politicians and public figures who watched as the flag-draped coffin was brought into the courtyard of police headquarters.
Ms Le Pen wants France to reintroduce border controls and deport all foreigners on a terror watchlist.
Mr Macron, an advocate of open borders, has urged French citizens not to give in to fear.
Originally from the Loire Valley region in central France, he had reportedly been serving in the capital since 2014.
On 13 November 2015, he was deployed to secure the area around the Bataclan concert hall after the attack by the so-called Islamic State group.
When the venue reopened last November with a concert by Sting, Mr Jugelé was there again, telling the US magazine People: "I'm happy to be here... We're here tonight as witnesses. Here to defend our civic values. This concert's to celebrate life. To say no to terrorists."
French President François Hollande has used a ceremony to honour a police officer slain in Paris last week to call for unity in the "long and difficult fight against terrorism".