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While it seems unlikely that Deligne's article has been translated, there are several alternative sources in English that may be of use, including:
Tate's article "Number-theoretic background" from volume 2 of the Corvalis proceedings. It provides a lot of introductory material on Weil groups (some of it taken from Deligne's paper).
Chapter 7 of Bushnell & Henniart's book ''The Local Langlands Conjecture for'' GL(2). It presents (with proofs) the material on Weil groups and their (Weil–Deligne) representations as well as proving the existence of the "local constants", thus covering a lot of what is in Deligne's article. It even has a proof of the ℓ-adic monodromy theorem previously only available in the appendix to Serre–Tate!
Tate's article Local constants, in Algebraic number fields: L-functions and Galois properties (Proc. Sympos., Univ. Durham, Durham, 1975), pp. 89–131. Academic Press, London, 1977.
[Anyone reading this should feel free to add more bibliographic information, further references, or additional commentary on the various suggestions.]