His trade representative said the US was “very concerned” that the tax “unfairly targets American companies”.
On Thursday the French parliament is due to approve a 3% levy on revenue made by such companies as Google and Facebook inside the country.
France argues that these firms currently exploit global tax loopholes.
Tech giants are able to locate their headquarters in low-tax countries where they declare most of their profits, thereby minimising their tax bill.
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The new tax would be retrospectively applied from early 2019, and is expected to raise about €400m ($450m; £360m) this year.
Any digital company with revenue of more than €750m – of which at least €25m is generated in France – would be subject to the tax.
What has the US said?
“[Mr Trump] has directed that we investigate the effects of this legislation and determine whether it is discriminatory or unreasonable and burdens or restricts United States commerce,” the statement from trade representative Robert Lighthizer said.
The US inquiry could pave the way for punitive tariffs, which Mr Trump has imposed on several occasions since taking office.
Previous investigations launched by Washington have covered European Union and Chinese trade practices.
The latest inquiry was welcomed by Republican Senate Finance Committee Chairman Chuck Grassley and Senator Ron Wyden, the senior Democrat on the panel.
“The digital services tax that France and other European countries are pursuing is clearly protectionist and unfairly targets American companies in a way that will cost US jobs and harm American workers,” they said in a joint statement.
Mr Lighthizer’s office will hold hearings over several weeks before issuing a final report and making recommendations.
Analysis by Dave Lee, BBC North America technology reporter
This “Section 301” investigation, as it is known, has been used before as a way of eventually implementing new tariffs on countries the Trump administration feels is taking the US for a ride.
If France is going to take hundreds of millions of euros from the pockets of American tech giants, the US argument might be, then why shouldn’t the US earn more money from what the French do in the US? It took the same view with China and has buried itself in a trade war that has destabilised relations and has the potential to escalate even further.
The digital tax is a risk for France, for it is now isolated. There had been talk of a Europe-wide tech tax, but talks fell down thanks in part to opposition from countries such as Ireland, which has benefitted from being able to attract tech firms to set up their European base in the country. Other countries – such as the UK, Spain and Austria – are considering similar moves, but France is furthest along.
One thing all sides agree on, however, is that in our modern, digital economy, the overhaul of how companies are taxed is long overdue.
France will be hoping for one of two outcomes. Either countries follow their lead and implement their own, independent laws, limiting France’s exposure. Or the move gives added energy to calls for a multilateral agreement on how digital firms should be taxed globally, putting an end to the squirreling-away of vast sums of money made by internet giants.
The technology industry lobby group ITI welcomed the investigation but cautioned against tariffs.
“We support the US government’s efforts to investigate these complex trade issues but urge it to pursue the 301 investigation in a spirit of international co-operation and without using tariffs as a remedy,” said Jennifer McCloskey, vice-president of policy.
Why target tech giants?
At present, they are able to pay little or no corporate tax in countries where they do not have a large physical presence. They declare most of their profits where they are headquartered.
The European Commission estimates that on average traditional businesses face a 23% tax rate on their profits within the EU, while internet companies typically pay 8% or 9%.
France has long argued that taxes should be based on digital, not just physical presence. It announced its own tax on big technology firms last year after EU-wide efforts stalled.
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An EU levy would require consensus among members, but Ireland, the Czech Republic, Sweden and Finland raised objections.
France’s new 3% tax will be based on revenue generated in the country, rather than on profits.
About 30 – mostly American companies – will pay it. Chinese, German, Spanish and British firms will also be affected.
The French government says the tax will end if a similar measure is agreed internationally.
The big tech companies have argued they are complying with national and international tax laws.