The three-day tie begins on 7 April, five days after the Miami Open, which is played outdoors on a hard court.
World number one Andy Murray, who sat out Britain's 3-2 victory over Canada in the Davis Cup World Group first round, is expected to play in Miami.
Britain beat France in the quarter-finals in 2015, when they won the title for the first time in 79 years.
Murray, 29, said earlier this month he expected to return against France after a break following his fourth-round exit from the Australian Open.
Rouen's Palais des Sports can accommodate 5,200 spectators.

There will also be daily reports after each session and contributions from the 5 live F1 team from the second test - as well as a special 5 live season preview show coming from Barcelona on March 3.
The 2016 season gets under way on 20 March, with the first race in Melbourne, Australia.
Circuit de Catalunya, Barcelona - 22-25 February
Circuit de Catalunya, Barcelona - 1-4 March
Ferrari - launched
Haas - launched
Force India - launched
Renault - launched
McLaren - launched
Mercedes - launched
Red Bull - launched
Sauber - 1 March
Toro Rosso - launched
Williams - launched
Manor - launched

The central bank's past efforts to spur growth have disappointed investors and there is expectation of more monetary easing from the meeting on Thursday.
Japan's Nikkei 225 index fell 0.5% to close at 17,353.28.
Embattled Mitsubishi Motors again saw its shares tumble, losing 9.6% over the day.
The Japanese car maker is engulfed in a scandal over falsifying fuel efficiency.
In China, the mainland benchmark Shanghai Composite closed 0.6% higher at 2,964.70 while in Hong Kong the Hang Seng ended up 0.5% at 21,407.27.
In South Korea, the Kospi index finished the day up 0.3% at 2,019.63, despite the country reporting its slowest quarter of economic growth in nine months.
In the January to March period the economy grew by 0.4% compared with the previous quarter, which was in line with expectations. On an annual basis, the economy expanded 2.7%.
In Australia, traders were equally cautious, and the ASX/200 index fell 0.3% to 5,220.64.

China's voting rights will rise to 6%, from 3.8% and IMF resources will double to about $660bn (Â£440bn).
This is the biggest shake-up since the IMF and the World Bank were set up to manage the post-World War Two economy.
China has set up the Asian Infrastructure Investment Bank as an alternative to the IMF and the WB.
The IMF reforms were agreed by its 188 members in the aftermath of the world financial crisis in 2010.
As China's voting rights rise, the US will see its share drop from 16.7% to 16.5%. The US also retains its veto power.
India's voting rights will rise to 2.6% from the current 2.3%.
The biggest losers are European economies which will see their voting rights diminished.
The US was behind the initiative to bring in the 2010 reforms in a bid to keep China happy.
But Republicans in the US Congress had been concerned at the diminishing US influence.
US Treasury Secretary Jacob Lew said in a statement: "The IMF reforms reinforce the central leadership role of the United States  in the global economic system and demonstrate our commitment to maintaining  that position."
IMF chief Christine Lagarde hailed the US adoption as a "a welcome and crucial step forward that will strengthen the IMF in its role of supporting  global financial stability".
And China's Central Bank said the reform "will improve the representation and voice of emerging markets and developing countries in the IMF and is conducive to protecting the IMF's credibility, legitimacy and effectiveness".
Last month, the IMF decided to include China's currency, the renminbi, as a reserve currency, alongside the US dollar, the euro, the yen and the British pound.
The IMF and the WB were conceived in 1944 at a conference in Bretton Woods, in the US state of New Hampshire.
The IMF aims to preserve economic stability and to tackle - or ideally prevent - financial crises. Over time, its focus has switched to the developing world.
The WB is the world's leading development organisation, working for growth and poverty reduction.
Great Britain's Davis Cup quarter-final against France in April will be played on an indoor clay court in Rouen.
[NEXT_CONCEPT]
You can follow Formula 1 testing on BBC Sport live, with track updates, expert analysis, social media reaction, debate, voting, the latest pictures and more from Barcelona.
[NEXT_CONCEPT]
Japanese shares fell for a second day as investors remained cautious ahead of a key Bank of Japan meeting later this week.
[NEXT_CONCEPT]
The US Senate has adopted long-awaited reforms to give emerging economies a greater say in how the International Monetary Fund (IMF) is managed.