Concerns have been raised after it emerged that Elizaveta Peskova, the daughter of Kremlin spokesman Dmitry Peskov, is interning for a French member of the European Parliament.
The right-wing MEP Aymeric Chauprade said Ms Peskova's internship with him began in November 2018 and would run until late April.
Fellow MEPs have objected to her having access to meetings and databases.
But a Parliament spokeswoman said Ms Peskova could only see public files.
Who is Peskova?
Elizaveta (Liza) Peskova has been studying law in Paris and is well-known socially. Her Instagram account has some 79,000 followers.
She has lived in France for several years and has not shied away from politics. She visited a shipyard two years ago in Crimea after the region was seized and annexed by Russia from Ukraine in 2014.
She has more recently posted observations on the French "Gilets Jaunes" (yellow vests) protests, comparing scenes in Paris at night to the computer game "Zombie Apocalypse".
Her father, Dmitry Peskov, is President Vladimir Putin's long-serving press secretary. Last month, Mr Peskov castigated the EU for imposing sanctions on two Russians blamed for the poisoning of Sergei Skripal and his daughter in the UK.
With European Parliament elections in May, there are fears that Russia may seek to influence the polls, as it has been accused of doing in France and elsewhere.
What are the concerns?
The question for critics is exactly what material Ms Peskova will have access to.
As a resident of France, she is entitled to work at the Parliament as an intern and her employer, Mr Chauprade, insists she has access only to details already in the public domain and nothing that is secret, not even the work of the EU-Russia delegation to which he belongs.
Mr Chauprade, a former international adviser of far-right leader Marine Le Pen, is a well-known supporter of Russia's seizure of Crimea. He is vice-chair of the Europe of Freedom and Direct Democracy Group led by UK Eurosceptic Nigel Farage.
A Parliament spokeswoman confirmed that Ms Peskova could go to any public meeting or delegation meeting as long as it was not restricted or held in private. Interns did not have access to confidential documents but would have access to the email database, she said.
The internship with Mr Chauprade was a contractual relationship with the MEP and not with the parliament itself, the spokeswoman said.
But Mr Chauprade is on the Parliament's security and defence subcommittee as well as the foreign affairs committee, so he will receive a number of key documents.
Latvian MEP Sandra Kalniete said there was no security clearance at the Parliament as there was at Nato. "The internship of Putin press secretary Peskov's daughter is contrary to any security standards," she told the country's public broadcaster, LSM.
French Socialist MEP Christine Revault d'Allonnes-Bonnefoy called the revelation "shocking".
"The daughter of the Kremlin's spokesman is not just anybody. I am surprised this hiring was validated by the parliament personnel service," she told the AFP news agency.