France is facing further political chaos after the country's latest prime minister, Sébastien Lecornu, resigned after just 26 days in the role. We'll hear from a French parliamentarian with the right-of centre party, Les Républicains - and we'll get the long view on French politics from veteran French journalist Christine Ockrent.

Also - as indirect talks begin between Hamas and Israeli delegations over the US-led peace plan for Gaza, we'll hear from an American go-between who knows the Hamas negotiators; and we look at what the appointment of Bari Weiss at CBS News says about the political weather surrounding journalism in the US.

(Photo: French outgoing Prime Minister Sebastien Lecornu, who presented his government's resignation to the French president this morning, leaves after he delivered a statement at the Hotel Matignon in Paris, France, October 6, 2025. Credit: REUTERS/Stephane Mahe)

The chief negotiator for Hamas is reported to be meeting Egyptian and Qatari mediators in Cairo ahead of indirect talks, later in the day, with Israeli negotiators in Sharm El-Sheikh. They're looking to determine a date for the start of a Gaza truce and create conditions for the first phase of the peace plan, in which the remaining Israeli hostages would be swapped for hundreds of Palestinian detainees.

Also in the programme: The French Prime Minister Sébastien Lecornu has quit. There is political turmoil caused by inconclusive snap elections; and this year's Nobel Prize for Medicine has been awarded to three researchers for discoveries on the human immune system.

(Photo: Smoke rises after Israeli air strikes at Tal Al Hawa neighborhood during an Israeli military operation in Gaza City, Gaza Strip, 06 October 2025. Credit: Mohammed Saber /EPA/Shutterstock)

The prime minister of Georgia has announced plans to outlaw the main opposition parties. Irakli Kobakhidze was speaking a day after anti-government protesters tried to storm the presidential palace. We hear from opposition activist Giga Lemonjava.

Also in the programme: Israel and Hamas prepare for indirect talks; and inside legendary guitar shop Regent sounds.

(Picture: Georgian opposition parties supporters clash with riot police during a rally after local elections in Tbilisi, Georgia, 04 October 2025. Credit: EPA)

Syria is holding its first parliamentary elections since the fall of Bashar al-Assad last December -- but the vast majority of the population can't vote and the president is choosing many of the candidates.

Also, can the US-led peace plan for Gaza work? We'll hear about the key negotiations due to begin in Cairo and ask whether it's feasible to expect Hamas to disarm. And a bigger question: when does anti-Zionism equate to anti-Semitism?

Plus a legendary guitar goes on display in a shop in London.

Picture: Voting begins for representatives of Syria's new parliament in Damascus on October 5, 2025. Credit: REUTERS/Khalil Ashawi)

Israel's prime minister, Benjamin Netanyahu, has said that diplomatic and military pressure have forced Hamas to agree to free the hostages it is holding. As Israel and Hamas prepare to take part in indirect talks in Cairo, Mr Netanyahu thanked Donald Trump for his peace plan.

Also in the programme: protests in Georgia; and 50 years of the Rocky Horror Show.

(Picture: Hostages Square 2-Year Rally - a large banner reads: 'It's Now or Never' - displayed in response to Trump's Gaza peace plan to end the war and the return of all the remaining hostages: The rally was held at Hostages Square to mark two years since the October 7 attacks. Credit: Hostages Families Forum)

A representative of the organisation told the BBC that Hamas accepted the proposal in principle - but wished to make some changes on a number of key points. We ask the experts what this might mean for a peace deal in the Middle East.

Also in the programme: rap star Sean 'Diddy' Combs sentenced to 50 months on sex-related charges in a New York court; prominent French economist Gabriel Zucman explains his proposal for a wealth tax; and the first female archbishop of Canterbury.

(Photo: Israeli military operation in Gaza City, 3 October 2025; Credit: MOHAMMED SABER/EPA/Shutterstock)

Dame Sarah Mullally has been named as the new Archbishop of Canterbury designate - the first woman to be chosen to head the Church of England.

It is the first time in nearly 500 years of history that the Church has nominated a woman as its head. We'll ask who Sarah Mullally is - and whether she can restore trust and unity in her church.

Also in the programme: A senior member of the Jewish community in the UK says Thursday's deadly attack in Manchester was a shock but no surprise; we'll hear about tourism creaking in Cuba; and a ravenous baby planet has been making headlines.

The British Prime Minister Keir Starmer says Britain must defeat what he called the "rising hatred of Jewish people", after a deadly attack at a synagogue. Two Jewish people were killed and four others injured after a car was driven towards worshippers at the site in Manchester. Police declared it a terrorist incident. They shot the suspect dead.

Also in the programme: Venezuela's opposition leader tells us she welcomes America's attacks on alleged drug smugglers, saying they'll force the President out. We look at protests in Morocco; and is Formula One getting too hot for the safety of its drivers?

(Photo: A member of the Jewish community holds a Torah at a police cordon in Manchester, Britain, 2 October 2025. Credit: Photo by Adam Vaughan /EPA/ Shutterstock)

Two people have been killed by a car that drove into a crowd outside a British synagogue on the Jewish holy day of Yom Kippur. Another man was stabbed at the site. We hear the latest news on the incident.

Also in the programme: a wide-ranging interview with the leader of the Venezuelan opposition, Maria Corina Machado, who is in hiding after being barred from last year's election; and a BBC analysis of Ukrainian drone attacks against Russian oil refineries.

We also hear about a new exhibition in Cambridge that sheds light on craftspeople in ancient Egypt.

(Photo: People gather near the scene following an incident outside a synagogue in Manchester, Credit: REUTERS/Temilade Adelaja)

EU leaders are meeting in Copenhagen under pressure to boost European defence after a series of Russian incursions into EU airspace, and days after drones targeted Danish airports.

Also in the programme: The International Red Cross has been forced to cease operations in Gaza City because of the intensity of the Israeli offensive; Jane Goodall, famous for her ground-breaking studies of chimpanzees, has died at the age of 91; and as one Hollywood star, Julie Andrews, turns 90, we'll hear about a new young actor who'll never grow old.

(Photo: Denmark has reinforced security for the summit and allies have beefed up air defences. Credit: Reuters)