LONDON, Jan 3 (Reuters) - European stock index futures pointed to a slightly lower open on Thursday, with some investors taking profits on 20-month highs following "overbought" trading conditions on some indexes, and as euphoria over the U.S. fiscal deal waned.

At 0705 GMT, futures for Euro STOXX 50, Germany's DAX and France's CAC were 0.1 to 0.3 percent lower.

The FTSEurofirst 300 index closed 2.1 percent higher at 1,157.40 points in the previous session, fuelled by approval by U.S. legislators of a deal to halt automatic spending cuts and tax hikes, which threatened to tip the world's biggest economy into recession.