Les Bleus, winners of the previous World Cup three years ago, had looked as though they might make light work of Wednesday's visitors when Antoine Griezmann scored in stunning fashion less than halfway through the first period.
But Ukraine regrouped at the interval and equalized through a fortuitous Presnel Kimpembe own goal before protecting a precious first point.
It was a far cry from their 7-1 friendly defeat to Didier Deschamps' men when the sides last met in October, even if the first half hinted at a similarly one-sided affair.
France were on the front foot from the outset and might have led before their 19th-minute opener as Olivier Giroud's first-time finish was deflected agonizingly off-target by Mykola Matvyenko.
There was no stopping Griezmann's stunning effort, though, curling inside the far post from the right corner of the penalty area.
The hosts had opportunities to add to their advantage heading into half-time, too, but Kylian Mbappe and Giroud each sent efforts over - the latter from a brilliant Benjamin Pavard cross - either side of a Kingsley Coman penalty appeal that saw Georgi Bushchan escape censure.
A huge slice of misfortune then saw France punished 12 minutes after the restart when Serhiy Sydorchuk's wayward shot earned a huge deflection off Kimpembe and crept into the net.
Les Bleus reclaimed complete control over the remaining minutes but could not forge a second goal or even a chance of note in an underwhelming start to their world title defense.