Valls spent Saturday in the former capital, Kyoto, and devoted most of the day to cultural questions.
He visited the Shimogamo shrine, which is surrounded by woods which, legend has it, favour conflict resolution and make it impossible to conceal a lie.
He also visited the city's manga museum and opened the city's Nuit Blanche (White Night), inspired by France's art all-nighter.
He was also to dine with Abe, an occasion for serious matters to be raised.
They were likely to include:
- Nuclear power - French nuclear giant Areva is in trouble and its reactor branch is currently being bought by the EDF power company. Valls indicated that he was not opposed to Mitsubishi Heavy Industries investing in the branch in an interview with Asahi Shimbun newspaper and sources travelling with him said it could invest in Areva's other activities, uranium mining for example. While 47 Japanese nuclear reactors remain closed following the Fukushima disaster, one reopened in August and another should be soon. Japan's nuclear industry has always been an important client for Areva and EDF.
- Free trade - Negotations are under way for a free-trade deal between the two countries but, Valls told Japanese media, "a lot remains to be done", especially on non-tariff barriers and public market access. The two countries are both suffering from sluggish growth, despite Abenomics in Japan and the policies of French Economy Minister Emmanuel Macron, who joins Valls along with about 60 French business leaders in Tokyo on Monday.
- Relations with China - Beijing has claimed control over most of the South China Sea, a subject of friction with its neighbours including Japan, which is looking at rearmament because of a perceived Chinese threat. This year it has built on several disputed islands, despite protests from them and the US. France wants international law to be respected, Valls told the press, but both he and President François Hollande had already visited China long before this trip. Valls also said that Chinese investments in Areva might be welcome, which may have ruffled some Japanese feathers.
- Science and technology - In Kyoto Valls and Abe were due to open a "Science Davos", the STS Forum, with 1,500 scientists attending. On Monday he was to inaugurate the Franco-Japanese Year of Innovation.