There are numerous reports about how Russia is financing right-wing politicians within the EU in order to unbalance the Union. But why doesn't the EU return the favor and start funding people like Alexei Navalny or Mikhail Khodorkovsky?
Russia already claims that "the West" is funding it's opposition, so it wouldn't give any more ammunition to Russian propaganda.
There are several points in your question which need to be separated.
First, this article you've linked asserts that there is a deliberate campaign from the Russian government which tries to influence the French elections. For this, various subjects are identified:
Let us assume that this is all true and uncontroversial (which it is not), and that the actions of all these subjects are not independent but orchestrated from the top, for which this article provides no proof whatsoever. Then we can already see that structure of the alleged influence: there is just little direct influence by the Russian government or Putin, but mostly over indirect channels such as other members of the Russian Parliament, NGOs, and state-financed media outlets. So these are the channels that we should also look into the other way round.
Secondly, you assume the EU does nothing to support Russian dissidents, which is untrue.
Official support directly from the EU is quite difficult. The EU has a complicated constitutional structure to reach political decisions, and a large bureaucracy. So official support by highest EU institutions, if it were intended, would also face various obstacles. There is an official program to support human rights, however it seems the usual EU bureaucratic nightmare to apply for such a grant, see e.g. the following old example.
There are examples of direct funding of Russian NGOs by the EU, see http://www.nytimes.com/2011/12/02/world/europe/russia-puts-pressure-on-elections-monitor-golos.html
Some of the authorities of the EU could, however, take personally a supporting role for dissidents. They are:
The head of the European Council, Donald Tusk
The head of the European Commission, Jean-Claude Juncker
The president of the EU parliament, until recently Martin Schulz
The EU high representative, Federica Mogherini.
I will here deal only with the last two.
Federica Mogherini has been criticized by a large group of the European security elite for taking a 'weak' stance against Russia, see here or enter link description here. Actually, on the list of signatories, there is Garry Kasparov, another Russian dissident. So you see here already some involvement between think tanks and a Russian dissident.
For Martin Schulz, a quick glance on the Khodorkovsky website (as of April 25 2017) shows that there are EU activities, for instance the Boris Nemtsov Forum in Brussels, where Martin Schulz, the then-presiding President of the European Parliament, was attending (see other speakers including other members of the EU parliament) The Nemzow Forum lists as its partners the major fractions of the EU parliament as well as the Friedrich-Naumann Foundation for Freedom which is related to the German Liberal Party.
The main influence into the internal business of foreign states actually happens via such think tanks and party political foundations. Especially German party political foundations have a long history of influencing the inner politics of foreign states, and particularly in supporting the opposition in states which oppose the foreign policy goals of the German government. I've provided already the connection of the Friedrich Naumann Foundation, similar connections can be found for other political party foundations in germany. That's why the Russian authorities also targeted them in a crackdown to prevent further meddling into the internal politics of Russia.
So as some commenters metioned before, the western powers first started by interfering into Russian politics, not least by their unequivocal support for Yeltzin, who even commanded tanks to shoot at the Parliament (can one be more anti-democratic than that? Yet, Putin is the bad guy and Yeltzin was an angel in the western press. But this is another story…)
