Of the 1,700 attempts, some 1,000 were "pushed back" by authorities and 700 were intercepted within the 650-hectare Channel Tunnel site, police added.
The officer was hit in the face by a stone apparently thrown by a Sudanese migrant, who was arrested. The policeman was taken to hospital for stitches.
The 1,700 attempts represented a major increase from the last few nights when only a few hundred were registered.
The chaos at Calais spiked last week when more than 2,000 attempts were made to breach the Eurotunnel defences and one person was killed, a Sudanese man in his 30s who was apparently crushed by a lorry.
At least 10 people have died since June in the rush to sneak into England, seen by migrants as an "Eldorado".
French police have bolstered their presence with 120 additional officers, which appears to be reducing the number of nightly attempts to storm the Eurotunnel premises.
The issue has become a cross-Channel political hot potato, with British Prime Minister David Cameron coming under fire for comments in which he referred to "swarms" of people seeking to get into the country.
Anger is also mounting in France over the issue.
Henri Guaino, a lawmaker from the opposition right-wing party Les Republicains, called on London to "do their share."
"There is no reason for these people to be stored -- if I may say this because it's almost that -- in France. It cannot go on like this," said Guaino.
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"The situation is fairly simple. Migrants come to Calais to get to England. England does not want them. Therefore the migrants pile up in Calais and try by whatever means they can to reach England."
Earlier this week, the British government pledged 10 million euros ($11 million) to improve fencing around the Eurotunnel rail terminal in Coquelles, outside Calais.
And Cameron, who has warned that the crisis could last all summer, promised "more fencing, more resources, more sniffer dog teams" to aid French police in their nightly cat-and-mouse game with the migrants.