vertically ascending bright light going on and off,that at 2 miles high remains on and shoots up int the stars very very very fast

We were on the beach late at night (Pampelonne),I was looking west in the direction of the maures a range of mountainous hills in southern france.I noticed a bright light ascending vertically, it was difficult to judge the distance as it was dark and although the light was bright (that of a shooting star perhaps),it was difficult to judge the size (obviously).As yet nothing strange but the light was going on and off as it went up (say 2seconds on and 2 seconds off)this happened approx. 10 times (going on and off).The strangest thing though,and here it is difficult for me to judge height as I wasn't exactly sure of the distance,but for arguments sake say at a distance of 6-10 miles and height of approx 2-3 miles the light suddenly remained on and shot up into the stars (from bright light to nothing in approx. 1 second) at an accelaration and velocity so extreme that I was sure no earth craft /jet /rocket could attain. I saw this alone the first time but instantly mentioned it to some of the friends that were with me,and pointed to where it had happened (luckily for me) exactly the same thing happened again, another one took off in exactly the same manner.They saw the second one but it didn't happen again. this is the only non explicable ufo sighting I've seen and to this day wonder what it was.I know that jets go up in pairs and they can switch their afterburners on and off but this was dead vertical and the final accelaration was far beyond any jet, of that I'm sure....Any ideas clues, any other sightings like this???
Date is approximate.  PD