Arthur Ashe, stricken by a cramp for the first time in his career, hobbled to a gutsy victory over Jan Kodes yesterday, but otherwise it was a bleak day for tennis-playing Americans in Paris.

Harold Solomon and Brian Gottfried, the only American finalists here since 1957, were upset in the third round of the French Open tennis championships.

Ashe, serving well and playing some of his finest clay court tennis, fought off three set points in the third set and a severe cramp in his right calf in the fourth to beat Kodes, 4-6, 6-3, 7-6, 6-4, in a 3-hour 20-minute match that delighted an overflow crowd of 15,417 at Stade Roland Garros.

That was only one of the grueling epics on a day of broiling sunshine and body- and mind-jarring matches that demonstrated graphically why the French is one of the most demanding of the world's major championships.

Solomon, runner-up to Adriano Panatta in 1976, lost his cool after blowing a huge lead and a set point in the second set and was beaten by the second set and was beaten by the unorthodox Chilean Davis Cupper, Han Gildemiester, 3-6, 7-5, 6-0, 6-4.

Gottfried, runner-up to Guillermo Vilas last year, missed far too many easy volleys and fell to qualifier Rolf Gehring, who aspires to make his Davis Cup debut for West Germany this month, 6-3, 6-7, 4-6, 6-3, 6-2. This was the longest match of the day: 4 hours 5 minutes.

Gottfried was seeded third and Solomon eighth in the field of 123. Another seeded American, No. 10 Dick Stockton, saved two match points before his uphill struggle against Balazs Taroczy of Hungary was suspended at dusk at two sets all.

In other matches, defending champ Vilas withstood a determined effort by 18-year-old French junior Yannick Noah, a native of Camerouns, who was "discovered" by Ashe during a State Department goodwill tour, 6-2, 4-6, 6-1, 6-1. Fifth-seeded Manuel Orantes of Spain ousted Tomaz Smid of Czechoslovakia, 7-5, 7-5, 6-2.

Tim Gullikson, the right-handed and higher-ranked of the touring twins from Onalaska. Wis, routed Californian Jeff Borowiak, 6-2, 7-6, 6-2, and Australian John Alexander overpowered Ricardo Cano of Argentina, 7-6, 6-2, 6-3. The other half of the third round will be played today.

Ashe, who had never beaten Kodes on clay, was outplayed by the energetic "bouncing Czech" in the first set, but then started to mix his game cleverly. He attacked fortrightly on his own serve, following first and second deliveries to the net. But on Kodes' serve, Ashe tried a variety of slices, spins, drop shots and changes of pace.

Ashe had the dour little man from Prague running in circles, lurching for shots he so frequently hits off-balance.

Ashe won the second set impressively and led, 3-0, in the third when Kodes started returning serve better and getting more depth with his ground strokes.

Kodes, 32, broke back to 2-3 on his sixth break point in a game that went to deuce eight times. He broke again for 6-5 with a forehand return winner down the line and a buzzing backhand cross-court pass.

Kodes had three set points on his own serve in the next game, but lost it on a double-fault after four deuces. He led, 5-3, in the tie breaker, but Ashe won the last four points. It provided again that Kodes can still whipcord shots, but his nerves are not what they were when he won here in 1970 and 1971, at Wimbledon in 1973, and twice reached the U.S. Open final.

After a 15-minute intermission, with Kodes serving at 2-2, 15-0 in the fourth set. Ashe stretched for a shot in his backhand corner and froze. A cramp had seized his left leg - a new experience for one of the leanest and most supple players in tennis.

Play was interrupted for some 2 1/2 minutes. A couple of ballboys ran over to aid Ashe, but he waved them away. The umpire asked if Ashe could continue. He gingerly took a few steps, stiff-legged and tentative, and limped back to the baseline.

Kodes held his serve at 30, but then it was he who fell apart, unable to exploit Ashe's limited mobility in the next three games. As sometimes happens against an injured player, Kodes tried not to make errors, but only threw off his own rhythm. He grew increasingly ragged and frustrated, and bickered with the crowd that was solidly behind Ashe.

Though limping badly, Ashe continued to pound his serve and come to the net for decisive volleys. He peld his serve to 4-4 climaxing a love game with a mighty ace, and broke Kodes at 15 with a forehand passing shot.

With his midcalf tennis sock rolled down around his right ankle to relieve pressure. Ashe served another love game to end the match. On the final point, he ambled in behind a second serve and put away a forehand cross-court volley to tumultuous applause.

"I'm just amazed that I did the right thing when the cramp hit me. It was a brand new experience for me," Ashe said. "I learned in the Boy Scouts and the Army that if a muscle cramps, you should stretch it out immediately.

"As it was, I'm surprised I won. I didn't think very much of my chances at that point. Jan tried to hit the ball down the middle instead of running me side to side, which surprised me, but that's not a bad strategy against a cramping player: Keep the ball in play, and wait for him to fall down.

"I think the cramp was more emotional than physical. This was the longest match I've played in some time, but I'm in good shape. I could have played five sets in practice or out on court No. 4 and never even felt it. But the center court has such a highly-charged atmosphere, you get caught up in all the people yelling and screaming."

Gottfried and Solomon were both paired against opponents they had never played before.

Gehrig, 22, had to win three qualifying matches to get into the tournament, and went five sets in each of the first two rounds. He is only No. 196 in the computer rankings of the Association of Tennis Professionals. He is regaining his condition and form after two hernia operations that sidelined him four months last year.

Gildemeister, 22, was born in Peru of German parents. He moved to Chile at age 2. He started to play tennis at 5, hitting with both hands because the racket was so heavy. He still hits two-fisted on the forehand and backhand, with great power and deception, using one hand on the serve, overhead and volley.

He is a streaky player who improved his game enormously in three years at the University of Southern California. He served for the match against Solomon at 5-3 in the fourth set and was broken, but broke Solomon for the match after two deuces in the next game. He forced a high-looping backhand wide off one of the ferocious rallies that characterized the final set.