Economyman -
Why cant you continue with Star Alliance?
I think you get status miles with each airline within the alliance. Star Alliance is great with Israel, because you have LH, LX, OS all in one program Miles and More - which is great for within Europe. If you fly to the far east you can fly on Thai's codeshare flights with LY and get Miles and more or other Star alliance FF program miles on those flights.
Next I would consider Skyteam - Since they have Af and you can use them to the Far East and obviously for your flights in France. To the US you have flights with DL and CO though you wont get status miles.
... and of course EL AL but try to compare how long it will take you to aquire Gold status on LY and how long it will take with Star Alliance.