Listen to French speech and pay attention to how the French pronounce the sound "R". Try to emulate them, to pronounce French words as they. Note that in contrast to the Russian sound "R" in French is not derived by the tip of the tongue, and root.
Right language, touch the root of the tongue edges the palate and pharynx. Do not press language to the sky too much – fairly light touch. Try to pronounce the sound "R" in the French manner. Most likely, at first you will have to turn out badly, but the regular exercise will bear fruit, and pronunciation will improve over time.
Say a few times the word "mine". Pay attention to how you pronounce the sound "x" in this word, and then try to pronounce it separately. When you are able to pronounce the sound separately, add voice and try to pronounce a voiced consonant, and not the dead. You should get the French sound of "p".
Type in your mouth a little water, slightly bend your head and start to gargle. When the water in the mouth begins to gurgle, try to pronounce the sound "g" as in Ukrainian the word "yeah". Then spit out the water and try again to say the same vibrating sound you said, rinsing a throat. Practice regularly until until you get results.
Select a song in French that you like and learn it. Try singing, pronouncing the sound "R" in exactly the same way as it sounds in the original.
Regularly record your own voice on the recorder, and then listen carefully to compare it with the French speech. So you can capture your progress, determine which exercises give the best results to improve your pronunciation. Keep training for as long as your "R" will start to sound the same as in the speech of the French.