One of the nice things about award tickets is that you can mix and match airlines.

So you could take CO or any other SkyTeam or CO partner carrier to your European stopover in CDG or AMS or FCO or wherever. Then you could take a SkyTeam nonstop to Israel, and any combination (or the CO nonstop) back from Israel.

Of course all of that is subject to availability, which tends to be VERY tight to/from TLV. I'd suggest calling CO and starting backwards from the segment to TLV. Look for availability on every Skyteam carrier from their European gateway (AMS, CDG, MXP, FCO, PRG) to TLV on the dates you can go. Then look for availability from the various USA gateways to your European gateway.

Finally, look for any combo that will get you home at the end.

For example, if you can find a seat on AF's CDG-TLV flight for an acceptable date, look for AF, CO, NW, and DL flights from all the US gateways that connect with your home town (presumably PDX?). AF flies to CDG from EWR, ATL, DTW, CVG, IAH, and LAX--all of which are only one stop from PDX via CO/NW/DL/AS.

In theory you could end up with an itin that looks like:

Travel Day 1: PDX-(DL)-CVG-(AF)-CDG
Travel Day 2: CDG-(AF)-TLV
Travel Day 3: TLV-(KL)-AMS-(NW)-SEA-(AS)-PDX



Finally, yes, all the SkyTeam flights between Europe and Israel are on narrowbody planes with crappy business class. And yes, KL has a long AMS stopover from the US to TLV (I did it twice last year). But KL's connections coming back are perfectly decent. And while 5:30am seems like an ungodly time to depart TLV, I find it helps a lot with jetlag, since I stay up all night beforehand, and sleep better on the plane. KL is far from the only one who leaves at that hour (when TLV is positively hopping).

Still, if you can get the CO nonstop to EWR on the way back, it's probably a better bet (especially in BF).