Montgomery County's leading Democrats endorsed the congressional candidacy of Peter Franchot yesterday, displaying party unity that would have seemed impossible a week ago.

Michael D. Barnes, who for eight years held the 8th Congressional District seat that Franchot is seeking, was joined at a news conference in Rockville by a long list of Democratic notables who proclaimed the freshman Takoma Park state legislator the party's best chance of recapturing the seat from Republican Rep. Constance A. Morella.

The outpouring of Democratic support was a clear boon to Franchot's candidacy. A newcomer to county politics, Franchot had gotten a cool reception from some key segments of the county's political establishment, which had been neutral until County Council member Michael L. Gudis began his ill-fated candidacy.

Gudis, a nine-year council member, had picked up some key endorsements, including that of County Executive Sidney Kramer, and was considered a front-runner for the Democratic nomination. But after a poor performance at a candidates' debate last week, he withdrew from the March 8 primary, saying that his council duties prevented him from becoming versed in the national issues of a congressional campaign.

Officials played down yesterday the party divisions and the seeming disarray Gudis' entry and exit brought to the party. County Council member Isiah Leggett said it was part of the normal political process in which a front-runner emerges.

Franchot faces four candidates in the primary: Rosemary Glynn, Ralph Shur, George Benns and James Walker Jr. Franchot's opponents have not held elective office and are not seen as having the financial or organizational strength to mount a strong challenge.

The theme of yesterday's show of support was that the Democrats stand the best chance of defeating the popular Morella by uniting behind one candidate. Barnes spoke of his own experience 10 years ago when he, then a relative unknown, unseated a Republican.

He said that Franchot, a former Capitol Hill staff member, is better qualified than he was and has the advantage of the party behind him 10 months before the general election.

Among those endorsing Franchot were County Council President Michael L. Subin, who had been a Gudis supporter; National Democratic Committeeman Lanny J. Davis, and Stewart Bainum Jr., who lost to Morella in 1986.

Noticeably absent was Kramer. Franchot said that he has spoken to Kramer and the executive was supportive but did not feel it necessary to make a formal endorsement now.