Packman (Moulton College) and Onojaife (Stowe School) started at full back and lock respectively, with Skelcey (Moulton College) and Peters (Oundle School) coming off the bench in the second half.
Despite conceding the first points, England silenced the home crowd by scoring three converted tries to go 21-3 up.
But any thoughts of a cruise to a comprehensive win were banished as France scored a pair of quick-fire tries to pull themselves back to 21-15, and although fly half Josh Sharp landed a penalty a third try from the hosts reduced the deficit to just two points just past the hour mark.
However Sharp landed another three-pointer with 10 minutes to play and England held on for their second successive win in the tournament.
"I'm delighted for all of the guys," said England head coach John Fletcher. "It was a great game and both sides played their part - I thought we played well for large periods and deserved to get the win. Full respect to France though, they had the crowd behind them and pushed us all the way."
However while the Under-18s had a successful weekend England's Under-16s fared less well, losing 20-24 to Italy Under-27s in Lichfield.
All five of the Saints' contingent saw action, with hooker Freddie Davison (Bedford School) scoring a first half try. He was one of three starters from the Saints' Elite Player Development Groups, centre Rotimi Segun (Northampton School for Boys) and fly half Paddy McDuell (Bedford School) the other two, with Henry Peck (Vandyke School) and Garth Spencer (Biddenham Upper School) both coming off the bench.
England Under-16s are back in action on Saturday, playing Wales Under-16s at Iffley Road, home of Oxford University RFC.