In an interview with pan-Arabic news channel Al-Jazeera quoted by state news agency APS, Tebboune said its ambassador, Said Moussi, would "soon be back in Paris".
"Our relationship with France is fluctuating," he said.
Algiers withdrew its envoy in early February after accusing its former colonial ruler of helping activist Amira Bouraoui's "clandestine and illegal exfiltration" from Algeria to France after she was sentenced to two years in jail for "offending Islam" and for insulting the president.
Algerian-French ties fell into crisis in late 2021 after controversial comments on Algerian history by French President Emmanuel Macron.
But Macron visited the vast North African country last August, signing a joint declaration with Tebboune to relaunch bilateral cooperation.
The Bouraoui affair has reignited tensions.
Algerian authorities have placed four people in pre-trial detention over the case, prosecutors said in February.
A prominent figure in a 2014 protest movement against then-president Abdelaziz Bouteflika's bid for a fourth term in office, Bouraoui was also involved in the Hirak protest movement which unseated him in 2019.
She was sentenced in June 2020 to two years in prison before being granted provisional release the following month, but banned from leaving Algeria.
- 'Point of no return' -
During the interview, Tebboune also addressed his country's relations with its regional rival Morocco, a year and a half after Algiers cut ties with Rabat, citing "hostile acts".
"We regret to see relations between Algeria and Morocco get to this stage," he said. "They've reached a point of no return and our position was reactive."
Algeria is deeply opposed to Morocco over Rabat's ties with and arms purchases from Israel, as well as over the Western Sahara dispute.
Morocco occupies most of the former Spanish colony and sees it as part of its sovereign territory, but Algeria backs the Polisario movement which seeks independence there.
Spanish premier Pedro Sanchez's government last year broke with decades of neutrality on the issue, declaring it now backed a Moroccan proposal for limited self-rule under Moroccan sovereignty.
Algeria responded by suspending a cooperation treaty with Spain.
But in Tuesday's interview, Tebboune said Algeria considers Madrid's move "an individual position on the part of the Sanchez government".
He added that trade between the two countries was ongoing, even though many Spanish companies say they have been hit hard by the suspension of the treaty.
The European Union's foreign policy chief Josep Borrell visited Algeria last week, calling for stronger energy cooperation with Africa's top gas exporter as well as enhanced security ties.
Borrell also said the EU and Algeria could "do better" on trade relations, calling for a solution "to obstacles (Algeria) introduced since June 2022 to commerce with Spain".