Beware the flight CDG-TLV will allow you only 1 bag to be checked, if somehow you get them to interline it for you there wont be a charge. Highly doubt that TLV will interline it for you on the return. So you can be paying for any bag twice, if its not interlined from the get go. can cost $100 per bag each way.

I also strongly suggest against using a charter as if anything goes wrong eg delays, they wont put you onto any other Carrier and you can lose your return CDG-EWR free seat, sure CO will understand and might allow you for a fee to return on a different date but thats if and only if there are free seats available on those other dates CDG in the summer, something I wouldnt count on even with the US$ in its grave.

That all said, how much is a tkt EWR-TLV, I doubt you will be saving much if you are gonna be paying 550 Euros for CDG-TLV-CDG portion.

Update; just checked with fares at $1650 ai that means you will be paying $860 for the CDG-TLV part. so you would be saving $790 by using miles only to CDG. Id spring for the EWR-TLV tkts and know that I got my 2 bags on w/o having to pay for any over the 1st and no hassles with will my bags make it and if they dont whos at fault and where are they.

2nd this is why it pays to have miles with more then 1 Carrier. I had the same for my April trip but CO wanted closer to $1900, so I cashed in some AA miles was originally going RJ in biz then when the dates didnt work out I was lucky to get TR in coach for 75k 10k more then BA but w/o the Fees that BA is known for and BA wasnt available