There is general relief in Europe that this partial "phase one" U.S.-China trade deal has been signed. Any easing of tensions between the two giants is seen as a positive move, even if most of the existing tariffs remain in place.

Initial reaction from the markets, though, was muted with European stocks opening flat on Thursday morning.

But there are also concerns here that, with the China deal out of the way, U.S. President Donald Trump may now turn his attention to Europe – which in the past he has called worse than China on some trade issues.

France's president, Emmanuel Macron, reacted to the deal saying he hoped it would not lead to new tensions between the U.S. and Europe.

"I hope it is a good dynamic. But I would not want this Chinese-American rapprochement to be an excuse to reopen a new chapter of U.S.-European tensions." Macron told reporters.

Read more: China, U.S. sign phase one trade deal

There is already an existing trans-Atlantic trade war with tariffs on European steel and aluminum.

Trump also imposed $7.5 billion of tariffs on European goods ranging from French wine and Italian cheese to Scotch whisky in retaliation to state subsidies for airplane manufacturer Airbus. The EU replied with taxes on U.S. orange juice, bourbon, jeans and motorcycles.

Now there are fears this could escalate further.

On 7 January, French finance minister Bruno Le Maire announced the U.S. and France had given themselves 15 days to resolve a dispute over France's proposed "digital tax," targeting big U.S. tech companies such as Google and Amazon.

Washington is threatening to place a 100 percent tax on French wine, cheese and luxury handbags, which could then lead to further retaliation.

EU-China relations

Another concern voiced here regarding the new trade deal is that since China has agreed to buy an extra $200 billion worth of goods, agricultural products and services from the U.S. over the next two years, will that mean China buys less from elsewhere, including the EU?

China is the EU's second largest trade partner after the U.S. and the EU is China's largest trading partner. The European Commission estimates that EU-China trade is worth more than a billion dollars a day. But there are a range of outstanding issues, with some difficult negotiations ahead. 

The two sides have been working on a comprehensive investment procedure for several years but it is proving difficult.

EU has called China a "systemic rival" and voiced concerns about investments from state-owned Chinese companies and whether to use Huawei's 5G communications technology.

China's ambassador to the EU, Zhang Ming, warned in a recent interview that Europe could face a backlash from Chinese entrepreneurs that would impact Chinese investments in the region.

Read more: China-U.S. trade dispute timeline: what happened so far?

"What I hope to see is that the EU will keep to the principles of multilateralism and free trade," Zhang said.

China, though, sees Europe as an important counter-balance to the U.S. and Beijing has declared 2020 "the year of Europe."

There are two major summits planned for 2020. First comes the regular one in April in Beijing, when Chinese Premier Li Keqiang will meet the new EU leadership. Then in September, President Xi Jinping will travel to Leipzig in Germany for a special summit hosted by the country's chancellor, Angela Merkel, and including all 27 leaders of the EU's member states.

It is increasingly looking like 2020 could prove a breakthrough year for Chinese European relations.