France launched Operation Turquoise in late June near the end of the window of the killings (June 23, approximately 100 days after April 7). The goal was ostensibly to act for humanitarian reasons. As it turns out, it’s widely accepted by French media and historians of the genocide that France became complicit in the killings. For example, once French troops reached Bisisero, they told the weakened Tutsi survivors there to wait for help. Three days later, Interahamwe militia had found the survivors (hidden thus far) and massacred them.

By creating a safe zone near the Congo, they allowed — literally allowed — organizers of the genocide to escape. They said that their mandate was not to arrest anybody, even war criminals. Many escaped into the Congo, and along with the humanitarian crisis it caused there (overflowing refugee camps), it provided a base from which the genocidaires could continue to attack the RPF. Africa’s World War by Prunier covers this.

If you search for Operation Turquoise, you’ll find more. In short, they indirectly helped the Interahamwe to kill more Tutsis and Twa, they protected genocidaires, and because they announced that they were intervening, it made it much less likely that other international UN forces would intervene (“the French are there — why do we need to send troops?”), according to Dallaire.

Leave None to Tell the Story by Alison Desforges and A People Betrayed by Linda Melvern both discuss Operation Turquoise. I don’t recall if there’s a book by Gerard Prunier (previously mentioned) that does so, but he would also be a reliable source as he was part of the French govt at the time and is currently a leading historian in the Rwandan genocide.

Also add to OP’s question, what was the role of Belgium?

Belgium took over Rwanda/ Burundi from Germany after WWI. The Tutsi-Hutu divide already existed (roughly 85% Hutu and 15% Tutsi), the Hutu were traditionally farmers and Tutsi were cattle herders. But Belgium made it more racial, measuring people's heads and other physical features, issuing identity cards based on who looked more European.

Right before Belgium left Rwanda, they saw the writing on the wall, that a democratic Rwanda would mean Hutu control and tried to switch sides, but by the early 1960's, they finally agreed to leave and the Hutu elected a Hutu president.

Now skipping ahead significantly to the early 1990s, during the Rwandan Civil War, there were UN peacekeepers being requested. But after (UN) America's problem during the Battle of Mogadishu, Somalia in late 1993, few countries were donating troops to UNAMIR, so Belgium signed on a significant number, breaking an "unwritten code" for a former colonial power to contribute a peacekeeping force to its old colony.

After the President's plane was shot down, 10 Belgian UN soldiers went to guard the Prime Minster and have her deliver a message for calm on the radio. They were eventually surrounded by Hutu extremist forces, along with 5 Ghanian UN soldiers. The Ghanians were let go, but the Belgians were killed, along with the PM.

Shortly after, Belgium, like the US in Somalia, pulled out its remaining forces (the majority of the forces) from Rwanda.

Lt Romeo Dallaire stayed with roughly 300 troops from Ghana, Tunisia and Bangladesh, even though he was instructed to also leave.

Sources:

• Power, Samatha, A Problem From Hell: America and the Age of Genocide, Basic Books, 2002.

• Hymowitz, Sarah and Amelia Parker, "History of the Hutu and Tutsis," American University Washington College of Law Center for Human Rights and Humanitarian Law.

• Preston, Julia, "Rwandans Confound U.N. Security Council," Washington Post, May 8, 1994.

EDIT: Formatting

This is a great question! Here in France academics are currently confronting the legacy of France in the 1994 genocide and a healthy debate is raging, including events at most major universities and a series of conferences examining the historical record. One of the most notable was the conference debate « La France au Ruanda, l'opération Turquoise en question » hosted at Sciences Po on 20 March between Admiral Jacques LANXADE, chef d'Etat-Major des armées during the genocide and Mr. Guillame ANCEL, a former officer of the Force d'action rapide on the ground in Rwanda. In it, Lanxade broadly confirmed the public narrative of France's actions, referring to Kagame's RPF as the « ménace FPR » and stating that the assassination of Habyarimana included French deaths that "demanded French justice" (translation my own) after stating that the French policy objectives in Rwanda pre-genocide were 1) supporting the implementation of the Arusha accords and 2) maintaining stability.

What is more interesting out of this debate was the testimony of Ancel. He opened his remarks with the incendiary phrase « je vous parle de la role de la France au génocide des Tutsis », perhaps giving you an idea of his perspective. He contended that the FAR (French special forces) were sent directly from Sarajevo to Kigali and that in fact France was engaged in a secret war against the RPF, that French forces were actually sent out into the countryside to find the RPF when they discovered the massacre for the first time and that their mission was to stop the RPF, not the génocidaires. It should not be surprising that this perspective was challenged quite heavily by Lanxade, but Ancel called out Pres. Mitterand, Minister Hubert Vedrine, and Lanxade all by name for effective complicity in the genocide of the Tutsis by the actions they chose to take during the slaughter.

Getting back more directly to your question, one must look first at France's relations with Rwanda prior to 1994. The Habyarimana regime and France enjoyed close relations--it could almost be said that France stepped into Belgium's shoes as the dominant European power in Rwanda, providing material and economic support to the state. France's activities in Rwanda broadly match up with their role in other francophone African states, comprising a broader foreign policy aim of successive French governments that was widely known as Françafrique. Most significantly among this support was French training of the Rwandan military. Allegations have been raised by several Rwandan sources that members of the Interahamwe received French training in the days leading up to the genocide. Due to the quality of records kept and the overlap between the pre-Arusha Accords Rwandan Army and subsequent Interahamwe, it would be virtually impossible to answer this question definitively, but a fair conclusion would be to say that it is likely that France provided military training to future génocidaires. This was not intentional, but a byproduct of France's support for the Hutu regime.

The second widely repeated accusation is that through Operation Turquoise, France protected the perpetrators of genocide and allowed them to escape. In this case it is important to remember, again, that the pre-genocide Hutu government was a strong French ally in the region. Coming out of the mess that was the breakup of Yugoslavia, French Pres. Mitterand was initially highly reluctant to intervene in Rwanda and when he finally chose to, the French leadership was adamant that it would not be within the confines of the Canadian-led UNAMIR peacekeeping mission already on the ground. The mandate of Operation Turquoise was to establish humanitarian safe zones in Kigali and rural parts of the country. The French did this, very quickly establishing an area from the border with Zaire roughly to Kigali under French military control. On the other side of the border, the French set up a command structure in Goma and took control of the Goma airport. Rwandans flowed into the French humanitarian zone and many of them crossed the border into Zaire. This included many members of the génocidaire government, who were able to take off in planes from the French military-controlled airport in Goma and for at least some time escape justice. Whether this represented an intentional act on the part of the French government, incompetence, or an effective inability to police who was moving where in the midst of the massive person flows is unclear. What is clear, however, is that the French government, possibly under the orders of Secrétaire général de la présidence Hubert VEDRINE (later Foreign Minister), sought to cover up its potential wrongdoing in this area. This veil of secrecy was maintained until fairly recently, and as recently as in 2017 Alain JUPPÉ, Foreign Minister in 1994 and then Presidential candidate, declared that there is no basis for accusing France of complicity.

In summary, whether maliciously or intentionally, France allowed the following three things:

1) Trained subsequent génocidaires as part of its military relationship with the Rwandan Army

2) Refused to work with UNAMIR to stabilize the country, rather pursued its own separate unilateral military engagement focused on preserving French interests in the country and hindering the RPF, which was seen by the French government as an adversary

3) Permitted the escape of members of the Hutu regime through the French-controlled Rwanda-Zaire border

One can fairly argue whether this means that France bears any direct complicity in the genocide. It is incontrovertible, however, that France made choices in several cases which strengthened the position of the Hutu extremists or allowed them to escape justice.

Some sources that informed this answer (some of these are more biased than others, but they represent a variety of perspectives):

Dallaire, Roméo, Shake Hands with the Devil: The Failure of Humanity in Rwanda, Random House Canada, 2003.

Lanotte, Olivier, La France au Rwanda (1990-1994): entre abstention impossible et engagement ambivalent, Heinemann, 2014.

Lanxade, Jacques, Quand le monde a basculé, Nil, 2001.

Verschave, François-Xavier, Complicité de génocide ?. La Politique de la France au Rwanda, La découverte, 1994.

Wallis, Andrew, *Silent Accomplice: The Untold Story of France's Role in the Rwandan Genocide *, IB Tauris, 2007.

Ed: Formatting

nothing much to add except to recommend "We Wish to Inform You that Tomorrow We Will Be Killed with Our Families" by Philip Gourevitch as I felt it to be a balanced summary of Europe's involvement (esp. France) in the genocide and has a few informative interviews with members of the UN and various affiliated governments.