Zelensky did make an important concession in advance of the meeting: He accepted a formula that calls for elections in separatist-held territories that would pave the way for a special, self-governing status in parts of Donetsk and Luhansk provinces.

But the devil, as always, is in the details. The Ukrainian side says it needs first to be fully in control of its own borders in order for those elections to happen. Right now, those parts of Ukraine's eastern borders are under the control of Russian-backed separatists.

Zelensky's willingness to talk with Putin, who annexed Crimea in 2014 and who has supported separatists in eastern Ukraine, infuriates many Ukrainians, however.

On Sunday, several thousand people held a demonstration in Kiev's Maidan Nezalezhnosti (Independence Square) to protest what they see as a potential "capitulation" to Putin.

Under a banner that read, "No elections in the Donbas until the implementation of security and de-occupation," speakers warned of "red lines" that should not be crossed by Zelensky in the Paris talks.

"We do want the war to stop, but we don't want peace at any price," Inna Sovsun, a member of the Ukrainian parliament, told CNN. "We want peace not on Putin's terms, but on Ukraine's terms. Because we are the ones who were attacked. Ukraine was attacked by Putin."

The Trump impeachment drama has also raised questions in Ukraine about whether US commitment to Kiev may waver. The US has provided military assistance to Ukraine, and Zelensky got a much-needed shot in the arm on Sunday, when he spoke by phone with Kristalina Georgieva, the managing director of the International Monetary Fund (IMF).

Georgieva informed Zelensky that the IMF would unlock a three-year, $5.5 billion loan program to shore up Ukraine's finances.

On Friday, the US embassy in Ukraine put out a statement in advance of the summit.

Officially, at least, the US still stands behind Ukraine.