Ireland still trail World champions South Africa by just under four rating points, but the battle for fourth spot in the rankings is now the tightest it has been for some time.
As the countdown continues to the Rugby World Cup in New Zealand, only 0.45 points separate Ireland and the French who are sixth.
France did improve their own rating by nearly a point following a 28-9 defeat of Wales at the Stade de France in the final match of this year's Six Nations, an outcome which increases their cushion over the Welsh in sixth spot.
Scotland, meanwhile, picked up their first win of the Championship against Italy, the 21-8 success at Murrayfield enough to avoid the wooden spoon on points differential.
The Scots remain ninth in the rankings, while the Azzurri stay 12th after failing to build on their historic win over France a week earlier.
IRB WORLD RANKINGS (as of Monday, March 21):
Last week's positions in brackets -
1(1) NEW ZEALAND 93.19 rating points
2(2) AUSTRALIA 87.45
3(3) SOUTH AFRICA 86.44
4(6) IRELAND 82.51
5(4) ENGLAND 82.48
6(5) FRANCE 82.06
7(7) WALES 79.55
8(8) ARGENTINA 78.97
9(9) SCOTLAND 77.35
10(10) FIJI 74.05
11(11) SAMOA 74.02
12(12) ITALY 73.54