The shares closed 11.5p higher at 105.5p, after rumours that the planned debt for equity conversion would be less harsh towards shareholders than first feared.
The move came after a formal confirmation by Eurotunnel that Sir Alastair Morton, the co-chairman, is not standing down at the annual meeting but will continue in office until the debt question is resolved.
There had been pressure from some banks, including NatWest, to force Sir Alastair out at the annual meeting.
Reflecting the fact that 75 per cent of Eurotunnel's shareholders are now French, Patrick Ponsolle, Sir Alastair's French opposite number, will become the sole executive co-chairman after Sir Alastair retires.
Eurotunnel is to appoint another British co-chairman to replace Sir Alastair when he does leave, but he will be a part-time non-executive. The announcement made clear that Sir Alastair was staying on for the time being at the request of the Eurotunnel board.
Two directors, Graham Corbett, the British finance director, and Berhard Thiolon, are to retire at the AGM.
Additional factors cited for the rise in the share price, which has been steadily recovering since its low of 63p on 3 April, included Eurotunnel's initiative in renewing the price war last week against ferry operators and comments by Mr Ponsolle that it was not unrealistic to expect an agreement with the banks in time for the annual meeting on 27 June.
A company spokeswoman in Paris said: "Today there is no more news than yesterday. We are looking at the rise and we say to each other that there is no real explanation for it. When we say that a deal is not unrealistic, that doesn't say that there is necessarily going to be a deal before June 27."
A stock market trader said: "There are a lot of buying orders from Japanese institutions on rumours about a debt restructuring."